im 


4 


A 


COMPENDIUM 


NATURAL   PHILOSOPHY 


ADAPTED  TO  THE  USE  Or 


THE    GENERAL    READER, 


AND   OF 


SCHOOLS    AND    ACADEMIES. 


BY  DENISON  OLMSTED,  A.  M. 

PIOFMSOR   Or   MATHEMATICS   AND  NATURAL  PHILOSOPHY  IN  YALE  COLLEGE. 


NEW    HAVEN: 

PUBLISHED  AND  SOLD  BY  HEZEKIAH  HOWE  &    CO. 

Sold  also  by  COLLINS  &  HANNAY,  New  York;  CARTER,  HENDEE  &  Co.,  Bo$- 

ton;  TRUMAN,  SMITH  &  Co.,  Cincinnati. 

1833.  ' 


Entered  according  to  Act  of  Congress,  in  the  year  1833,  by  DENISON  OLMSTED,  in  the  Clerk's 
office  of  the  District  Court  of  Connecticut. 


Printed  by  Hezekiah  Howe  &  Co. 


' ' 


PREFACE. 


IT  is  the  object  of  this  work,  to  present  to  the  general  reader,  and 
to  the  more  advanced  pupils  in  our  Schools  and  Academies,  the  most 
important  PRACTICAL  RESULTS  of  Natural  Philosophy,  (without  the 
demonstrations,)  in  as  condensed  and  intelligible  a  form  as  possible, 
and  to  exemplify  them  by  a  great  variety  of  applications  to  the  phe- 
nomena both  of  nature  and  art. 

Within  a  few  years  past,  great  efforts  have  been  made,  especially 
in  England,  to  divest  science,  as  far  as  possible,  of  every  thing  tech- 
nical, and  to  render  its  most  important  practical  principles  intelligible 
to  every  well  informed  reader.  The  profoundest  truths,  are  often 
capable  of  being  expressed  in  terms  that  are  plain  and  easily  under- 
stood, although  the  reasonings  by  which  those  truths  were  investiga- 
ted, and  the  proofs  by  which  they  are  established,  may  involve  re- 
fined and  intricate  mathematical  processes.  Leaving,  therefore,  the 
demonstrations  to  such  as  are  professionally  devoted  to  science,  it 
has  been  proposed  to  take  the  results  only  for  the  use  of  the  general 
reader,  and  to  show  their  applications  to  the  useful  arts,  and  to  the 
explanation  of  natural  phenomena. 

By  this  means,  not  only  will  scientific  knowledge  be  far  more 
widely  diffused,  but  the  useful  discoveries  of  science  may  thus  be 
rendered  available  to  artists,  and  others,  who  will  reduce  them  to 
practice.  It  was  with  this  view,  that  the  scientific  treatises  in  the 
Library  of  Useful  Knowledge,  were  prepared  and  published,  at  the 
suggestion,  and  under  the  auspices,  of  the  present  enlightened  Lord 
Chancellor  of  England.  Some  of  those  treatises  are  well  adapted 
to  the  purpose  in  view ;  others  are  ill-suited  to  the  wants  of  the  gen- 
eral reader,  and  they  were  evidently  composed  by  men  little  con- 
versant with  the  tastes  and  attainments  of  those  for  whom  they  were 
professedly  written.  Individuals,  also,  of  profound  acquirements  and 
of  high  standing  in  the  scientific  world,  have  embarked  in  the  same 
enterprise.  Among  the  most  successful  of  these,  is  Dr.  Lardner  of 
the  London  University,  whose  writings  on  the  several  branches  of 
Mechanics,  and  Leclures'on  the  Steam  Engine,  are  among  the  best 


IV  PREFACE. 


attempts  at  reducing  scientific  principles  to  the  popular  standard. 
Dr.  Bigelow's  "Elements  of  Technology,"  is  a  highly  useful  and 
respectable  work  of  the  same  class;  and  a  few  others  might  be  men- 
tioned which  are  deserving  of  a  similar  character.  Many  of  the 
writers,  however,  who  have  published  scientific  works  designed  for 
general  reading,  or  for  schools,  make  their  works  easy  of  compre- 
hension, merely  because  they  introduce  into  them  nothing  but  the 
simplest  and  most  superficial  parts  of  the  subjects  of  which  they  treat, 
and  consequently  give  to  the  learner  nothing  but  a  smattering  of  sci- 
ence,— too  little  either  to  enlighten  his  mind,  or  to  qualify  him  to  ap- 
propriate the  resources  of  science  to  his  practical  benefit. 

During  the  years  1831  and  1832,  the  writer  published  a  work  on 
Natural  Philosophy,  in  two  volumes  8vo.  designed  as  a  text  book  for 
students  in  college.  He  has  been  frequently  solicited  to  prepare  a 
volume  like  the  present,  suited  to  the  purposes  of  the  general  reader, 
and  adapted  to  a  portion  of  the  students  in  our  High  Schools  and 
Academies,  who  have  not  made  the  attainments  in  mathematics  re- 
quisite for  perusing  the  larger  work.  Such  a  work  is  the  volume 
now  offered  to  the  public.  It  contains  the  most  important  principles 
of  Natural  Philosophy,  with  extensive  practical  applications,  and  re- 
quires no  farther  attainments  in  mathematics  than  a  knowledge  of 
common  arithmetic. 

The  writer,  while  he  has  studied  plainness  and  perspicuity,  has  not 
deemed  it  either  necessary  or  expedient,  to  expound  the  doctrines  of 
Philosophy  in  a  juvenile,  not  to  say  puerile,  style,  with  the  view  of 
making  it  more  intelligible  or  more  attractive  to  young  minds.  Such 
a  style  he  believes  to  be  no  more  intelligible  than  the  ordinary  style 
of  phflosophical  writing ;  and  he  would  desire  the  youngest  student 
of  philosophy  to  receive  the  impression,  that  the  study  owes  its  at- 
tractions to  its  own  inherent  dignity  and  utility, — to  the  elevation  of 
its  truths,  and  to  their  great  practical  importance. 

The  elevated  course  of  study  adopted  in  some  of  our  schools, 
both  male  and  female,  requires  a  corresponding  improvement  in  the 
books  prepared  for  their  use.  In  many  of  these  seminaries,  it  is 
hoped  that  there  will  be  pupils  sufficiently  advanced  in  mathematics, 
to  read  the  more  elaborate  works  on  Natural  Philosophy ;  while  a 
still  larger  proportion,  perhaps,  will  find  the  present  treatise  sufficient- 
ly extensive  for  their  use. 


PREFACE. 


The  numerous  Voluntary  Associations  formed  in  various  parts  of 
our  country,  for  philosophical  inquiry,  will,  it  is  believed,  find  the 
present  work  well  adapted  to  promote  their  objects ;  especially,  on 
account  of  its  numerous  practical  applications  of  the  principles  of 
science  to  the  arts,  and  the  purposes  of  life.  Professional  gentle- 
men, also,  and  others  of  liberal  education,  will  find  this  small  treatise 
favorable  for  reviewing  subjects,  which,  in  the  couhe  of  their  colle- 
giate education,  they  may  have  studied  in  a  more  difficult  form. 
They  may,  moreover,  meet  with  some  things  here,  which  the  pro- 
gress of  the  science  has  brought  to  light,  since  the  time  when  (hey 
were  students  in  philosophy. 

To  teachers  who  may  use  this  book,  the  writer  begs  leave  to  re- 
commend a  free  use  of  the  Analysis.  This  furnishes  a  clue  to  all 
the  leading  truths  contained  in  the  text ;  and  the  learner  can  be  con- 
sidered as  having  gained  entire  possession  of  the  contents  of  the  book, 
only  when  he  is  prepared  to  give  a  correct  and  full  account  of  each 
of  these  heads.  This  will  be  done  most  effectually  by  frequently 
reiterating  the  Analysis  during  the  perusal  of  the  text,  at  the  com- 
mencement or  at  the  close  of  each  lesson.  By  this  means,  each  of 
the  heads  will  afterwards  call  up,  by  association,  the  train  of  ideas 
of  which  they  are  the  index ;  and  thus  the  leading  truths  and  prac- 
tical applications  of  philosophy,  will  be  indelibly  engraven  on  the 
memory  of  the  learner.  These  heads,  moreover,  will  serve  as 
common  places, — a  depository,  where  he  may  advantageously  ar- 
range all  his  subsequent  acquisitions  on  the  same  points. 

With  respect  to  the  sources  from  which  the  materials  of  this  vol- 
ume have  been  drawn,  they  are,  for  the  most  part,  the  same  as  those 
of  the  larger  work,  where  they  are  indicated  in  the  margin.  Such 
references  are  omitted  here  for  want  of  room. 

Some  remarks  will  be  found  at  the  end  of  the  book,  on  the  sub- 
ject of  philosophical  apparatus,  which  may  contain  useful  informa- 
tion for  teachers. 

Yale  College,  Aug.  1,  1833. 


ANALYSIS.* 


PART  I. 

MECHANICS. 


CHAPTER  I. 

PRELIMINARY    PRINCIPLES. 

Page. 

NATURAL  PHILOSOPHY  defined, 
Term  Law,  how  used,      .  • 
Natural  Philosophy  divided  into  four 

parts, 

MECHANICS  defined, 
Body,  particle, 
Statics  and  Dynamics, 
Hydrostatics  and  Pneumatics, 
Two  essential  properties  of  matter,        2 
Extension  defined, 
Impenetrability  do. 

GRAVITY  do.  .  .3 

Force  of  gravity,  how  related  to  the 

quantity  of  matter,      .  .          3 

Extent  to  which  the  law  of  gravity 

prevails, 

Attraction  of  Gravitation  reciprocal,  8 
Weight  defined,  .  .  4 

Gravity,  how  related  to  the  distance,  4 
Case  of  a  body  within  a  hollow  sphere,  5 
Force  of  attraction  below  the  Earth's 

surface,  ...          6 

INERTIA  defined,  .  6 

how  related  to  the  quantity    . 

of  matter,          .  7 

CHAPTER  II. 


MOTION    AND    FORCE. 

Absolute  motion, 

Relative       do. 

Apparent     do. 

Uniform      do. 

Accelerated  do. 

Uniformly  accelerated,    . 

Space,  how  related  to  time  and  velo- 
city, 

Time,  how  related  to  space  and  velo- 
city, .  ;;* 

Velocity,  how  related  to  time  and 
space,  .... 


Page, 

Examples,  9 

Momentum  defined,         .            .  10 

how  related  to  velocity 

and  quantity  of  matter,             .  10 
Force  defined,       .            .            .11 

how  measured, 

Examples,            .           .           .  11 

CHAPTER  III. 

THE    LAWS   OF   MOTION. 

FIRST  LAW,         .  12  f 
Expresses  the  doctrine  of  inertia  in 

four  particulars,             .             .  12 
Proofs  of  the  tendency  of  bodies  to 

continue  in  rest  or  in  motion,   .  13 

Illustrations  of  the  tendency  to  rest,  13 

Do.                       do.     to  motion,  14 
Tendency,   by  inertia,  to  uniform 

motion,  .  .  .15 

Proved  by  At  wood's  Machine,     .  16 

Atwood's  Machine  described,      .  16 
Tendency  of  bodies  to  move  in  right 

lines,      .            .            .            .  .  17 
Why  natural  motions   are   usually 

curved,  .  .  .17 

Centrifugal  force  defined,           .  17 

Illustrations  of  it,               .             .  17 

Whirling  Tables  described,        .  18 
Centrifugal  force,  how  related  to  the 

specific  gravity  of  a  body,         .  18 
Do.  to  the  velocity,           .            .  18 
Spheroidal  figure  of  the  planets,  19 
In  what  part  of  the  earth  does  cen- 
trifugal force  act  most,              .  20 

How  it  affects  the  weight  of  bodies,  20    

SECOND  LAW.  2Ty 
Proofs  that  motion  is  proportioned  to 

the/orce,                                    .  21 
Proofs  that  motion  is  in  the  direction 

of  the  force,       .  .  .21 

Proofs  that  the  smallest  force  can 

move  the  greatest  body,           .  22     ^-^ 

THIRD  LAW,       .  22  \ 


*  This  copious  table  of  contents  is  designed  to  answer  the  purpose  of  questions.  In  pre] 
for  examination,  the  learner  is  requested  to  be  ready  to  give  a  full  account  of  each  of  these 
repeating  definitions  especially  with  the  greatest  correctness  and  precision. 


V111 


ANALYSIS. 


Page. 

Illustrations,          .  .  .28 

Collision  of  two  equal  bodies  moving 
in  the  same  direction,  .  24 

Ditto  moving  in  opposite  directions,    24 

Elastic  and  Non-elastic  bodies  de- 
fined, .  .  .  .25 

Examples  of  each,  .  .        25 

Velocity  lost  or  gained  by  the  collis- 
ion of  perfectly  elastic  bodies,  25 

Case  of  two  equal  balls  A  and  B, 
when  A.  overtakes  B,  .  .25 

Do.  when  A  and  B  meet  from  oppo- 
site directions,  .  .  .25 

Do.  when  A  strikes  upon  B  at  rest,      25 

This  law  applicable  to  cases  of  press- 
ure and  mutual  attraction,  .  26 

Sum  of  all  the  motions  in  the  world 
estimated  in  one  and  the  same  line,  26 

Illustrations  of  this  principle,        .         26 

A  great  momentum  obtained  in  two 
ways,  .  .  .  .26 

The  body  which  gives  the  blow,  re- 
ceives an  equal  shock,  .  27 

Cases  where  action  and  reaction  de- 
stroy each  other,  .  .  •  28 

Proofs  of  the  Laws  of  Motion,     .        28 

CHAPTER  IV., 

VARIABLE    MOTION. 

Variable  Motion  defined,  .  29 

Falling  bodies,  why  they  fall  towards 

the  center  of  the  earth,  «  .  29 

Spaces  described  by  falling  bodies, 

how  related  to  the  times,  .  30 

How  far  does  a  body  fall  from  rest  in 

ont  second,  .  .  .30 

Impetuosity  of  falling  bodies,  .  31 
Motion  of  a  body  moving  with  the 

last  acquired  velocity,  .  31 

Spaces,  how  related  to  the  acquired 

velocities,  .  .  .31 

Case  of  a  body  projected  perpendicu- 
larly upwards,  .  .  32 
Case  of  a  body  projected  downwards,  32 
Laws  of  falling  bodies,  how  proved 

by  experiment,  .  .  33 

Curvilinear  motion  of  projectiles,  34 
Revolution  of  the  moon  round  the 

earth,  .  .  .  .35 

Gravity  detected  in  small  masses,  35 

CHAPTER  V. 

COMPOSITION  AND    RESOLUTION  OF 
MOTION. 

Simple  and  compound  motion,  36 

Motion  of  a  body  acted  on  by  two 

forces  in  different  directions,  36 

When  the  two  forces  acting  sepa- 


Page. 

rately  would  make  a  body  describe 
the  two  sides  of  a  triangle,      .        37 
Illustrations  of  this  principle,       .         37 
When  the  forces  would  make  the 
body  describe  all  the  sides  of  a 
polygon  except  the  last  side,    .        38 
When  the  forces  would  make  the 
body  describe  all  the  sides  of  a 
polygon,  .  .  .39 

Resolution  of  a  given  force,         .        39 
Sailing  of  a  ship,  .  .        40 

Case  of  a  body  acted  on  by  three 
forces  corresponding  to  the  three 
sides  of  a  triangle,  .  .  40 

Principle  illustrated  by  a  kite,      .        41 
When  does  a  body  describe  a  curve,      41 

CHAPTER  VI. 

CENTER   OF    GRAVITY. 

Center  of  Gravity  defined,          .        42 
Utility  of  its  doctrines,     .  .        42 

Center  of  gravity  of  regular  plane 

figures,  ,  .43 

To  find  it  by  experiment,  .        43 

A  body  resting  on  its  center  of  gravity,  44 
To  find  the  distance  of  the  center  of 
gravity  of  a  number  of  bodies  from 
a  given  point,   .  .  .45 

Supposition  of  all  the  matter  of  a 
body  concentrated  in  the  center 
of  gravity,  .  .  45 

Motion  of  the  center  of  gravity  of  a 

system  of  bodies,  .  .        46 

Ratio  of  the  weights  of  two  bodies 

balanced  on  their  center  of  gravity,  46 
When  will  bodies  standing  on  a  hori- 
zontal plane  remain  stable  or  fall,      46 
Position  of  the  line  which  joins  the 
point  of  suspension  and  the  cen- 
ter of  gravity  when  a  body  is  at 
rest,        ....        47 
A  body  revolving  vertically  around 
its  center  of  gravity  at  rest  only 
in  two  points,    .  .        47 

Illustrations  of  bodies  stable  and  un- 
stable,   .  .  .  .40 
Motions  of  animals,  how  related  to 

the  center  of  gravity,    .  .        49 

Hope  and  Wire  dancing,  .        49 

Stability  af  vegetables,     .  .        50 

Center  of  gravity  not  changed  by 

the  mutual  action  of  bodies,    .        50 
Problems  on  the  center  of  gravity,      50 

CHAPTER  VII. 


PROJECTILES    AND    GUNNERY. 

Projectile  defined,  .  .        51 

Random        do.     .  .  .        51 


ANALYSIS. 


IX 


Page. 

Random,  when  greatest,  .  51 

o'f  a  body  thrown  horizontally,  51 
Curve  described  by  projectiles,  .  52 
Theory  of  projectiles  inapplicable  to 

practice,  .  .  .52 

Experiments  of  Robins,    .  .        63 

Velocity  of  a  musket  ball,  .         54 

of  a  cannon  ball,  .         54 

Ratio  of  the  weight  of  powder  to  that 

of  the  ball,  .  .54 

Carronadef,  .  .  .55 

TVindage,  .  .  .55 

Rifles,  principle  on  which  they  act,  55 
Ricochet  firing,  ...  56 

CHAPTER  VIII. 

MACHINERY. — THE    LEVER. 

Tools,  machines  arid  engines,        .        56 
Maphines,  their  use  among  the  an- 
cients,   .  .  .  .56 
Mechanical  Powers,  the  elements  of 

machinery,         .  .  .     '    57 

LEVER  defined,     .  .  .57 

Fulcrum,  Power,  Weight,  defined,  57 
Axioms,  .  .  .  .57 

Levers  of  three  kinds,       .  .         58 

Compound  Lever  defined,  .        59 

When  do  the  power  and  weight  bal- 
ance each  other,  .  .  59 
Examples,  .  .  .60 
Balance,  what  kind  of  lever  is  it  ?  61 
Description,  .  .  .61 
Construction  of  a  perfect  balance,  62 
Sensibility  of  certain  balances,  .  63 
Bent  Lever  Balance,  .  .  63 
Steelyards,  construction  and  principle,  64 
Spring  steelyards,  .  .  64 
Compound  steelyards  described,  65 
How  to  find  the  weight  of  a  body 

too  heavy  for  the  steelyards,      .         65 
Proportion  of  a  load  shared  between 

two  bearer?,       .  .  .65 

Examples    of    levers,    single    and 

double,  .  .  .66 

Bones  of  animals,  their  mechanical 
construction,      .  «  .67 

CHAPTER  IX. 

MACHINERY  CONTINUED. — WHEEL 
WORK. 

WHEEL  AND  AXLE  described,  68 

Law  of  equilibrium,  .  .  69 
Different  modes  of  applying  the 

power,  .  .  .  .69 

Compound  Wheel  and  Axle,  law  of 

equilibrium,  .  .  69 

Principle  of  the/Msee  of  a  watch,  70 

Examples,  .  .  .  '.*  .  70 


Page. 
Communication  of  motion  by  wheel 

work,  ....  71 
Different  modes,  .  .  71 

Regulation  of  velocity  by  wheel 

work,  .  .  .  .73 

Illustrated  by  clock-work,  .  75 

Wheel  carriages,  the  advantages  of 

wheels,  .  .  .76 

Height  of  the  center  of  the  wheel,  77 
Position  of  the  line  of  draught,  77 

Most  advantageous  mode  of  coupling 

horses,  .  .  .77 

CHAPTER  X. 

MACHINERY     CONTINUED. PULLEY, 

INCLINED      PLANE,      SCREW,      AND 
WEDGE. 

PULLEY  defined,  .  .        78 

Fixed  pulley,  its  advantage,  .  78 
Fire  escapes,  .  .  '.  78 

Movable  pulley,  law  of  equilibrium,  79 
Examples,  .  .  .80 

INCLINED  PLANE,  law  of  equilib- 
rium, .  .  .  .80 
How  it  modifies  motion,  .  .  80 
Illustrations,  .  .  .81 
Railways,  construction  and  principle,  82 
Use  in  locks,  .  .  .82 
Law  of  gravity  in  the  inclined  plane,  82 
Velocity  acquired  in  descending  the 

plane,     .  .  .  .83 

SCREW,  its  analogy  with  the  inclined 

plane,     .  .  .  .84 

Law  of  equilibrium,          .  .         85 

Use  and  application  of  the  screw,  85 
Hunter's  screw,  construction  and 

principle,  .  .  .86 

Micrometer  screw,  .  .         87 

Example  of  a  remarkable  combina- 
tion of  the  mechanical  powers,        88 
WEDGE,  its  analogy  with  the  inclin- 
ed plane,  .         88 
Law  of  equilibrium,          .  .        89 
Use  and  application  of  the  wedge,        89 
Its  relation  to  friction,      .             .        89 
Comparative  velocities  of  the  power 

and  weight  in  all  machines,      .         90 
Illustrated  in  each  of  the  mechanic- 
al powers,          .  .  .90 

CHAPTER  XI. 

MACHINERY    CONCLUDED. 

Boast  of  Archimedes,      . .  .92 

No  momentum  gained  by  machinery,  92 
Its  real  advantage,  \nfour  particulars,  93 
Regulation  of  machinery,  its  impor- 
tance,    .  .  95 


B 


ANALYSIS. 


Page. 

Regulators,  large  machines  them- 
selves, .  .  .  .  .  95 
Do.  Pendulum,  .  .  .96 
Do.  Fly  wheel,  .  .  .96 
Fly  used  to  accumulate  motion,  97 
Whether  it  increases  the  force  of  a 

machine.  .  .  .97 

Rectilinear  motion,  how  produced,  98 
Gearing,  spur  gearing,  spiral  gearing,  98 
Revel  gearing,  .  .  ,  98 

Universal  joint,      .  .  .99 

Ratchet  wheel,     .  99 

Eccentric  wheel,  .  .        99 

Crank,       .  .100 

CHAPTER  XII. 

PENDULUM STRENGTH  OF   MATERI- 
ALS— FRICTION. 

Three  important  applications  of  the 

pendulum,        .  .  .         100 

Pendulum  defined,         .  .        100 

Center  of  suspension,  center  of  oscil- 
lation, .  .  .101 
Vibrations  performed  in  equal  times,  101 
Times  as  the  square  roots  of  the 

length,  .  .  .        101 

Length  of  a  pendulum  vibrating  sec- 
onds,    .  .  .  .102 
Do.  vibrating  once  an  hour,        .         102 
Times  of  vibration,  how  related  to 
the   distance   from  the  center  of 
the  earth,        .            .            .102 


Page, 
Use  of  the  pendulum  to  measure  the 

figure  of  the  earth,     .  .        103 

Ditto,  as  a  standard  of  linear  meas- 
ure,     .  .  .  .103 
STRENGTH  OF  MATERIALS,  prac- 
tical importance  of  the  subject,       103> 
Strength  of  a  beam,  to  what  propor- 
tioned,             .             .             .103 
A  triangular  beam  stronger  when 

resting  on  its  broad  base,  .  104 
Strength  of  a  bar  in  the  direction  of 

its  length,        .  .  .        104 

Lateral  strength  of  a  beam,  how  re- 
lated to  its  length,       .  .104 
Tendency  to  fracture,  in  a  horizon- 
tal beam,  to  what  proportioned,       105 
Tendency  of  large  structures  to  fall 

by  their  own  weight,  .        106 

Comparative  strength  of  hollow  and 

solid  cylinders,  .  •        106 

FRICTION,  its  origin,      .  .         107 

Experiments,  how  made,  .        109 

Effect  of  extent  of  surface,         .        109 

of  pressure,          .  .        109 

of  remaining  in  contact,          109 

Friction    between    surfaces  of  the 

same  and  different  kinds,  .  110 
Friction  at  first  starting  a  load,  110 
Friction  at  different  velocities,  .  110 
Comparative  friction  of  sliding  and 

rolling  bodies,  .  .        Ill 

Friction  wheels  described,  .  Ill 
Methods  of  diminishing  friction,  112 
Friction,  its  use  in  machinery,  .  112 


PART  II. 


IfYDROSTATICS, 


CHAPTER  I. 

FLUIDS    AT    REST. 

Page. 

Fluid  denned,     .  .  .        114 

Hydrostatics  defined,      .  .        115 

Equal  pressure  of  fluids  in  all  di- 
rections, .  .  .         115 
Effects  of  a  Now  upon  any  part  of  a 

fluid 115 

Hydrostatic  Press,  construction  and 

principle,         .  .  .116 

Explanation  of  its  great  power,  117 

Surface  of  «^fluid  at  rest,  .         117 

Levelling,  .  .  .         118 

Relation  of  pressure  to  the  depth,      118 
Pressure  of  a  column  of  water  8,  64 

and  96  feet  deep,          .  .119 

Do.  1  and  5  miles  deep,  .        119 

Illustrations  of  this  pressure,      .         120 


Page- 
Compression  of  water  at  the  depth 

of  1000  fathoms,  .  .120 

Pressure  of  a  fluid  against  a  surface 

in  a  perpendicular  direction,          121 
Level  of  a  fluid  in  opposite  arms  of  a 

tube,    .  .  .        •••  .        121 

Water  rises  as  high  as  its  source,  122 
Aqueducts  of  the  Romans,  .  122 
Pressure  of  a  column  of  fluid  upon  a 

horizontal  base,  .  .        122 

Hydrostatic  Paradox, 
SPECIFIC  GRAVITY  defined,  124 

Standard  for  liquids,  do.  for  gases,  124 
Loss  of  weight  in  water,  .  124 

To  find  the  specific  gravity 
Ditto  when  the  body  is  lighter  than 

water,  .  •        125 

To  find  the  specific  gravity  of  K- 

quids,  .  .        125 


125 


ANALYSIS. 


XI 


Page. 
Heights  of  two  fluids  in  equilibrium 

in  opposite  arms  of  a  tube,       .         126 
How  much  water  does  a  floating 

body  displace,  .  126 

Specific  gravities  of  various  bodies,    127 
Estimation  of  a  ships'  weight  by  the 

quantity  of  water  displaced,     .         128 
Swimming,          .  .  .128 

Force  with  which  a  body  will  as- 
cend or  descend  in  a  fluid,      .        128 
The  Camel  described,     .  .         129 

Stones  raised  by  ice,        .  .         129 

Structure  of  life  boats,    .  .         129 

Estimation  of  the  magnitudes  of  ir- 
regular bodies,  .  .         ISO 

CHAPTER  II. 

FLUIDS    IN    MOTION. 

Hydraulics  defined,         .  .         130 

Velocity  of  fluids  in  different  parts 

of  a  pipe  of  unequal  bore,       .         130 
Rivers,    false    doctrine    applied    to      # 
thern,  .  .  .  .131 

Cause  of  the  increased  velocity  dur- 
ing a  freshet,    .  .  .         131 
Cause  of  the  increased  momentum,    181 
Slow  motion  of  rivers — examples,      131 
Velocity  of  a  spouting  fluid  compar- 
ed with  that  of  a  falling  body,       132 
Quantities  of  water  from  a  spout, 


Page, 
how  related  to  the  depth,         .        132 

Velocity  of  the  fluid  uniformly  re- 
tarded as  the  vessel  empties  itslf,    133 

Clepsydra,  its  construction  and  prin- 
ciple,   .... 

A  vessel  delivers  double  the  quanti- 
ty when  kept  constantly  full, 

Curve  of  a  spouting  fluid, 

Random,  when  greatest, 

Friction  of  fluids., 

Effect  of  a  pipe  attached  to  the  ori- 
fice,    .... 


133 

133 
134 
134 
134 


135 


CHAPTER  III. 


CAPILLARY   ATTRACTION — RESIST- 
ANCE   OF    FLUIDS — WAVES. 

CAPILLARY  ATTRACTION  defined,  136 
Size  of  the  tubes,  .  .         136 

Height  of  the  liquid,  how  related  to 

the  diameter  of  the  bore,         .         136 
Phenomena  explained  by  capillary 

attraction,         .  .  .137 

RESISTANCE  OF  FLUIDS  how  re- 
lated to  the  velocity,    .  .         138 
Illustrations  of  this  principle,      .         138 
WAVES,  their  nature,     .  .         139 
how  produced,  .         140 
Depth  to  which  the  agitation  extends,  140 
Jlccumulation  of  waves,  .        141 
Questions  in  Hydrostatics,          .        141 


PART  III. 


PNEUMATICS. 


CHAPTER  I. 

MECHANICAL    PTOPERTIES    OF   AIR. 

Page. 
143 
143 
143 
144 
144 
144 
144 
145 
145 
145 


Pneumatics  defined, 

Vapors  and  gases  distinguished, 

Air  material,       .  .        :    . 

Air  a  fluid,          .  .  «  . 

Air  an  elastic  fluid, 

Illustrations  of  these  propositions, 

AIR  PUMP  described,     . 

Valve  defined,     . 

Piston  and  Cylinder, 

Mode  of  producing  a  Vacuum,    . 

Principle  of  the  air  pump  explained,  146 

Pressure  of  the  air  illustrated,    .         147 

Elasticity  do.         i"  '        .         147 

Relations  of  air  to  sound  and  com- 

bustion,  .  .  .148 

CONDENSER  described,  .        148 

Air-Gun,  ,  .  .        149 


Page- 
Diving  Bell,  .  .  149 
Barometer  described,  .  .  150 
Torricellian  Vacuum,  .  .  150 
Pressure  of  the  atmosphere  on  a 

square  inch,     .  .  .        151 

Pressure  in  a  square  foot,  .  151 
Graduation  of  the  barometer,  .  151 
Indications  of  weather,  .  .  152 

Mean  Pressure  of  the  atmosphere,    152 
Range  of  the  barometer  ia  the  equa- 
torial and  polar  regions  compa- 
red,     .  .  .  .152 
Use  of  the  barometer  to  measure 

heights,  .  .  .152 

Relation  between  the  pressure  and 

space,  .  .  .153 

Relation  between  the  density  and 

pressure,          .  .153 

Relation  between  the  elasticity  and 
density,  .  .  .153 


Xll 


ANALYSIS. 


CHAPTER  II. 

THE     ATMOSPHERE. 

Page. 

Weight  of  the  entire  atmosphere,       154 
how  ascertained,  .         154 

Law  of  decrease  in  density  on  as- 
cending from  the  earth,  .         155 
Rarity  at  the  height  of  7  miles,  155 
do.            49  and  100  miles,  155 
Increase  of  density  on  descending 

into  the  earth,     '  .155 

Density  at  the  depth  of  34  and  48 

miles,    ....         155 
Effect  of  heat  and  cold  on  the  baro- 
meter, .  .  .156 
Term  of  Perpetual  Congelation,          156 
Comparative  heights  in  different  cli- 
mates,              .            .            .        157 
Cold  of  the  upper  regions  of  the  at- 
mosphere,        .            .            .        157 
Air,  how  put  in  motion,    .             .         157 
Ventilation  of  Mines,     .             .158 
How  smoke  ascends  in  a  chimney,      159 
Draught,  how  increased  or  diminish- 
ed,                    .             .             .         159 
Jlmount  of  air  that  should  traverse  a 

fire,       .  .  .  .160 

Winds,  their  general  cause,  .  160 
Land  and  Sea  breezes  explained,  161 
Trade  Winds  described  and  explain- 
ed, .  .  .  161 
METEOROLOGY,  .  .  162 
Capacity  of  air  for  moisture,  how 

increased  and  diminished,         .         162 
Dew,  the  cause  explained,          .         163 
its  unequal  deposition,        .         163 
Fogs,  how  produced,       .  .         163 

Clouds,  their  analogy  to  fogs,      .         164 
Rain,  how  produced,       .  .         164 

Effect  of  constant  and  variable  winds 

respectively,     .  .  .         164 

Hail,  how  produced,        .  .         165 

Hail  storms,  climates  where  they  oc- 
cur,      .  .165 

CHAPTER  III. 

MECHANICAL    AGENCIES    OF    AIR 
AND  STF-AM. 

Syphon  described,            .  .  166 

its  principle,       .  .  166 

Suction  Pump  described,  .  167 

its  principle,  .  167 

Height  to  which  it  will  raise  water,  168 

No  force  g«jned  by  it,  .  .    168 

Forcing  Pump  described,  .  168 


Page. 

Forcing  Pump,  its  principle,      .         169 
Fire  Engine  described,  .         169 

STEAM  ENGINE,          , .  .         169 

Property  of  steam  on  which  its  me- 
chanical agencies  depend,        .         170 
Elasticity  ot  steam,  its  relations  to 

temperature  and  density,         .        170 
Great    elasticity    of    steam    when 

heated,  .  .  171 

Steam  Engine  described  in  all  its 

parts,  ,    . 

Economy  of  steam,          .  .         173 

Improvements  of  Watt,  .         173 

Description  from  the  plate,         .         174 
Steam  engines    which   act  expan- 
sively, .  .  .        176 
Self-regulating  powers  of  the  steam 
engine,             .             .  .177 

CHAPTER  IV. 


ACOUSTICS. 

Acoustics  defined,            .            .  177 

Cause  of  sound,               .            .  178 
Vibrations  of  a  string  performed  in 

equal  times,     .            .            .  178 

Vibrating  body  in  wind  instruments,  179 

Pitch  depends  on  four  circumstances,  179 

Bell,  its  change  of  figure  in  vibrating,  180 

Propagation  of  sound,    .             .  180 

Air,  the  usual  medium,  .            .  180 

its  agency  explained,            .  181 

Conducting  power  of  solid  bodies,  182 
Manner  in  which  sound  passes  from 

one  medium  into  another,       .  182 

Velocity  of  sound  per  second,     .  183 

Estimation  of  distances  by  sound,  183 

Conducting  power  of  liquids,     .  184 

Stethoscope,  its  construction,      .  185 

Reflexion  of  sound,          .             .  185 

Echo,  how  formed,          .             .  185 
Effect  of  the  furniture  of  a  room  on 

sound,        .                    .             .  186 

Rolling  of  thunder  explained,    .  187 

Speaking  Trumpet  explained,  187 

Musical  sounds,  how  produced,  188 

Musical  intervals,           .            .  189 
Why  musical  sounds  have  ratios  to 

each  other,  .  .189 
Melody  and  harmony  defined,  .  189 
Chords,  how  produced,  .  190 
Use  of  discords  in  music,  .  190 
Theory  of  stringed  instruments  ex- 
plained, .  .  191 
Do.  wind  instruments,  .  .  191 
Do.  mixed,  as  the  organ,  .  191 


ANALYSIS. 


Xlll 


PART  IV. 


ELECTRICITY. 


CHAPTER  I. 


GENERAL    PRINCIPLES. 

Page. 

Electricity  defined,        .  .         192 

How  manifested,  .  .         192 

When  a  body  is  said  to  be  excited,       192 
Do.  electrified,  192 

Conductors  and  non-conductors  de- 
fined, .  192 
Electroscopes  and  Electrometers  do.  192 
Pendulum  Electrometer  described,  192 
Gold  Leaf  do.  .  .  193 
Electricity,  how  produced,  .  193 
Properties  when  excited  from  glass 

and  amber  respectively,          .         194 
When  bodies  attract,  when  repel,      195 
Two  electricities  produced  simulta- 
neously, .        V.  •         196 
Comparative  conducting  power  of 

bodies,  .  ;        196 

Insulation,  how  effected,  .        197 

Sphere  of  influence  and  sphere  of 

communication,          .  »        198 

Induction  defined,  .  .        198 

CHAPTER  II. 


ELECTRICAL    APPARATUS. 

Object  of  electrical  machines,  .  199 
Cylinder  Machine  described,  .  199 
-flmalgam,  how  composed,  .  200 
Plate  Machine  described,  .  201 
Quadrant  Electrometer,  .  202 
How  to  construct  a  cheap  apparatus,  202 
Cement,  how  composed,  .  202 
Experiments  with  the  electrical  ma- 
chine, .  .  203 
Force  of  electrical  attraction  and  re- 
pulsion at  different  distances,  205 
Electricity  confined  to  the  surface,  205 
Leyden  Jar  described,  .  .  205 
Discharging  Rod,  .  ...  206 
Shock  imparted  by  the  Jar,  .  206 
History  of  the  Leyden  Jar,  .  206 
Experiments  with  the  Jar,  .  207 
How  charged,  .  .  .  207 
State  of  the  opposite  sides,  .  208 
Outside  must  be  uninsulated,  .  208 
Second  Jar  charged  from  the  first,  208 
To  charge  a  Jar  negatively,  .  208 
Two  Jars  charged  oppositely,  must 

have  their  outsides  connected,  209 

Electrical  spider,            ..           .  209 


Page. 

Charge  of  a  Jar,  how  divided,  .  209 
Office  of  the  coatings  of  a  Jar,  210 

Charge  of  a  Jar  long  retained,  .  210 
Effects  of  the  Leyden  Jar  explained,  210 

CHAPTER  III. 

ELECTRICAL  LIGHT— BATTERY — ME- 
CHANICAL AND  CHEMICAL  AGEN- 
CIES OF  ELECTRICITY. 

Electrical  Light,  when  it  appears,  211 
How  produced,  .  .  .  212 

How  the  spark  passes  in  a  vacuum,  212 
Do.  in  condensed  air,  .  .  213 

Do.  through  various  media,  .  214 
Illuminated  figures,  how  produced,  214 
Origin  of  electric  light,  .  .  214 

Battery  described,          .  .        216 

Great  battery  of  Haarlem  described,  216 
Its  effects,  .  217 

Sound  of  an  explosion,  how  produ- 
ced, .  .  .  .217 
Rending  of  bodies  by  electricity,  217 
Expansion  of  fluids  by  do.  .  218 
Chemical  effects  enumerated,  .  218 
Motions  instantaneous,  .  .  219 
Selects  the  best  conductors,  .  219 
Preference  of  a  shorter  route,  .  220 
Influence  of  points,  .  .  220 

CHAPTER  IV. 

EFFECTS  OF  ELECTRICITY  UPON  ANI- 
MALS— LAWS  OF  ELECTRICAL  PHE- 
NOMENA. 

The  electric  shock,  how  communi- 
cated, .  .  .220 
Effects  in  proportion  to  the  charge,     221 
The  shock,  how  given  to  a  number 

of  persons,       .  .  .         221 

Effects  of  taking  the  shock  on  the 

insulating  stool,          .  .        221 

Shock,  how  given  to  any  part  of  the 

system,  .  .  .         222 

Application  of  electricity  to  medicine,  223 
Medicated  tubes,  . *  .  223 

Medicinal  properties  of  this  agent,      223 
!  Cause  of  electrical  phenomena,          22o 
j  Probability  of  the  existence  of  a  pe- 
culiar electric  fluid,     .  .        224 
!  Properties  of  a  fluid   exhibited   by 
electricity,        .             .  .         225 


XIV 


ANALYSIS. 


Page. 
The  two  hypotheses  of  electricity 

compared,  .  .  226 

Arguments  in  favor  of  the  doctrine 

of  one  fluid,  .  .  .226 

Do.  of  two  fluids,  .  .  228 

CHAPTER  V. 

ATMOSPHERICAL  ELECTRICITY — 
THUNDER  STORMS — LIGHT- 
NING   RODS. 

How  the  electrical  state  of  the  at- 
mosphere is  ascertained,          .        229 
Mode  of  drawing  electricity  from 

the  clouds,        .  .  .        229 

Experiments  made  in  France,    .        229 
Analogies  between  electricity  and 

lightning,         .  .  .        230 

First  experiments  of  Franklin,  231 

Source  of  atmospherical  electricity,    232 
Thunder  Storms,  leading  facts  res- 
pecting, .  .  .        233 
cause  of,         .         234 
Lightning  Rods,  how  constructed,    234 
their  efficacy,          235 


CHAPTER  VI. 

PRECAUTIONS  FOR  SAFETY  DURING 
THUNDER  STORMS — ANIMAL  ELEC- 
TRICITY— CONCLUDING  REMARKS. 

Page. 
Liability  of  solitary  buildings  to  be 

struck,  .  .  .236 

Liability  of  ships  and  barns,       .         236 
Silk  dresses,  how  far  they  afford  pro- 
tection, .  .  .        236 
Feather  beds,  do.            .            .        236 
Danger  of  taking  shelter  under  a 

tree,     .  .  .  .237 

Tall  trees,  their  influence  in  protect- 
ing houses,       .  .  .        237 
Chimnies,  their  liability  to  be  struck,  237 
Electricity  of  the  Torpedo  and  Gym- 

notus,  .  .  .238 

The  Torpedo  described,  .        238 

The  Gymnotus   do.         .  .        238 

The  Silurus  electricus,  . 
Electricity  of  furred  animals,     .        240 
Electrical  light  from  pointed  objects,  240 
Agencies   of  electricity   in  natural 
phenomena,     .  .         >  :i        241 


PART  V. 


MAGNETISM. 


GENERAL    PRINCIPLES. 

Page, 

Magnetism  denned, 
Magnets,  loadstone,          .  .        242 

Jtttractive  power,  when  discovered,  242 
Directive  do.  .  -  .  242 

Poles  of  a  magnet,  axis,  .        243 

Needle  how  prepared   for  experi- 
ments, . 
Four  leading  properties,  .        243 

CHAPTER  I. 

MAGNETIC    ATTRACTION. 

Mutual  attraction  between  iron  and 

the  magnetic  pole,  .  .  244 

Other  metals  that  are  attracted  by 

the  magnet,  .  .  •  244 

Action  of  similar  and  dissimilar 

poles,  .  •  •  .244 

Magnetic  Induction  explained,  .  245 
Effects  of  induction  upon  the  nearer 

and  the  remoter  end  of  a  piece  of 

iron,  .  .245 

The  power  of  the  magnet  increased 

by  action,  .  .  246 

Effect  of  a  strong  magnet  upon  the 

poles  of  a  weaker  magnet,       .        246 


Page. 

Effect  when  the  north  pole  of  a  mag- 
net is  placed  on  the  center  of  an 
iron  bar,  .  .  246 

Do.  when  placed  on  the  center  of 
an  iron  disk,  .  .  .  246 

Magnetism  exists  only  between  the 
opposite  poles  of  magnets,  .  247 

Relations  of  soft  iron  and  hardened 
steel  to  magnetism,  .  .  247 

How  the  process  of  magnetising  is 
promoted,  .  •  248 

How  the  virtues  of  a  magnet  are  im- 
paired, .  .  .248 

Case  of  a  steel  bar  magnetized  by  in- 
duction when  separated  into  parts,  248 

Effects  compared  with  those  of  elec- 
tricity, .  .  248 

Force  of  magnetic  attraction  at  differ- 
ent distances,  .  .  249 

Magnetic  power  confined  to  the  sur- 
face, .  •  249 

CHAPTER  II. 

DIRECTIVE    PROPERTIES    OF    THE 
MAGNET. 

Effect  on  a  needle  when  suspended 
near  the  pole  of  a  magnet,  249 


ANALYSIS. 


Page. 

Action  of  a  magnetic  bar  on  iron  fi- 
lings,  .            .            .            .250 
Declination  or  variation  of  the  nee- 
dle,      ....  250 
Course  of  the  line  of  no  variation,  251 
Actual  variation  of  the  needle  at  sev- 
eral places,       .             .             .  251 
Diurnal  variation,            .             .  251 
Dip  of  the  needle,           .             .  252 
Magnetic  intensity  defined,       .  252 
How  measured,   .            .            .  252 
Earth  itself  a  magnet,     .            .  253 


Page. 

Magnetism  of  the  violet  rays,    .        254 
Electricity    and    Magnetism,    their 

analogies,          .  .  .        254 

Several  methods  of  making  artificial  * 

magnets,          .  .  .        255 

Horse  shoe  magnets,  their  construc- 
tion and  advantage,      .  .        256 
Kater's  rule  for  making  magnets,       257 
Compass  described,          .  .        258 
Mariner's  do.       .            .  .        259 
How  it  maintains  its  horizontal  po- 
sition,               .            .  .259 


PART  VI. 


OPTICS. 


PRELIMINARY  OBSERVATIONS   AND 
DEFINITIONS. 

Page. 

Optics  defined,    .  ".*        261 

Luminous  bodies  of  two  kinds,  261 

Kays  of  light  proceed  in  right  lines,  262 
Velocity  of  light,  .   .     '   .        263 

How  estimated,  .  .        263 

Intensity  of  light  at  different  distan- 
ces,     .  .:       264 

CHAPTER  I. 


REFLEXION   OF    LIGHT. 

Reflexion  defined,  .        :  •;•.-•••      264 

Mirrors  and  speculums,  j.        264 

Angles  of  incidence  and  reflexion 

defined,  ..  .  .         265 

Their  relations  to  each  other,      .        265 
Reflexion  from  plane  mirrors,  incli- 
nation of  the  reflected  rays,    .         266 
Image,  distance  behind  the  mirror, 

and  magnitude,  .  .        266 

Velocity  of  the  image  compared  with 

that  of  the  mirror  when  revolving,  267 
Reflexion  of  an  object  between  two 

parallel  mirrors,  '.'.."•'*"  *  '  268 
Do.  between  two  inclined  mirrors,  268 
How  to  judge  of  the  qualities  of  a 

mirror,  .     •   ;*».;«•.         .        269 

Proportion  of  reflected  rays  from  wa- 
ter, glass,  &c.  .        269 
Reflexion  from  concave  mirrors,         270 
General  office  of  concave  mirrors,       270 
Several  cases  according  to  the  posi- 
tion of  the  radiant,       .  .         270 
Experiments  with  a  candle  placed 

before  a  concave  mirror,         .        271 

Use  of  concave  mirrors  by  showmen,  272 

Do.  as  burning  instruments,       .        273 

Reflexion    from  convex  surfaces — 

general  office  of  a  convex  mirror, ,  273 


Page. 

Several  cases,      .  .  .        274 

Images  formed  by  convex  mirrors,     274 

CHAPTER  II. 

REFRACTION    OF    LIGHT    BY     LENSES 
AND    PRISMS. 

Light  passing  from  a  rarer  into  a 

denser  medium,  .  .        275 

Do.  from  a  denser  into  a  rarer  me- 
dium,   ....        275 
Illustrations  of  these  principles,          275 
Comparative    refracting   powers   of 

different  media,  .  .        276 

Various  lenses  defined,    .  .        276 

Office  of  a  convex  lens,  .  .        277 

Do.      concave  lens,  .        277 

Images,  how  formed  with  the  con- 
vex* lens  when  the  radiant  is  pla- 
ced at  different  distances,  277 
Radiant  must  be  farther  from  the  lens 

than  the  focus  of  parallel  rays,        278 

Spherical  aberration  explained,     .    279 

Prism  described,  .         280 

Course  of  a  ray  of  light  through  a 

prism.  281 

CHAPTER  III. 

SOLAR  SPECTRUM COLORS. 

Different  refrangibility  of  the  rays  of 
light,  .  .  281 

Method  of  producing  the  solar  spec- 
trum, .  .  282 

Simple  rays  no  longer  change  color 
by  refraction,  .  .  283 

Composition  of  solar  light,      .  284 

Prismatic  rays  united  to  form  white 
light,  *.  14  .  .  284 


XVI 


ANALYSIS. 


Page. 

Colors  produced  by  the  mixture  of 
others,  .  285 

Rainbow  described,     .  .  286 

Position  of  the  spectator  with  respect 
to  the  sun  and  the  bow,  .  288 

Cause  of  the  inner  bow,  .  289 

Do,  outer  bow,  .  289 

How  the  line  from  the  sun  to  the 
eye  of  the  spectator,  passes  with 
respect  to  the  bow,  .  290 

Height  of  the  bow  when  the  sun  is 
on  the  horizon,  .  .  291 

How  high  is  the  sun  when  the  top 
of  the  bow  just  comes  to  the  hori- 
zon? ...  291 

Peculiar  bows  seen  on  high  moun- 
tains, ...  291 

Colors  of  bodies,  their  general  cause,  291 

CHAPTER  IV. 

VISION. 

Circular  image  of  the  sun  shining 
into  a  dark  room  through  an  orifice 
of  any  shape,  .  .  292 

Camera  obscura,  how  formed,  293 

Picture  formed  by  a  lens  in  the  win- 
dow shutter,  .  .  294 
The  Eye,  its  parts,      .            .  295 
Contrivance  in  the  crystalline  lens 

for  preventing  spherical  aberration, 296 
Protrusion  of  the  cornea,  its  advan- 
tages, ...  297 
Extent  of  horizontal  vision,     .            297 
How  the  distinct  vision  of  objects  at 

different  distances  is  effected,         297 
Perfection  of  the  eye,  .  298 

Peculiar  structure  of  the  eyes  of  dif- 
ferent animals,         .  .  298 
Use  of  convex  spectacles,        .  300 
Do.    concave,  do.,     .  300 
How  distances  and  magnitudes  are 
estimated,     .            .  300 

CHAPTER  V. 

MICROSCOPES. 

Microscope  defined,  .  .  303 

Simple  Microscope,  how  it  aids  the 

eye,  ...  303 

Why  it  increases  the  distinctness 

and  size,  .  .  •  304 

Effect  of  shortening  the  focal  distance 

upon  the  Magnifying  power,         305 


Page. 

Do.  upon  the  field  of  view,     .  305 

Diamond  and  Sapphire  Microscopes, 

their  great  excellencies,      .  306 

Fluid  Microscopes,     .  .  307 

Perspective  Glass  described,  308 

Magic  Lantern        do.  .  311 

Solar  Microscope      do.  .  312 

Discoveries  of  the  Solar  Microscope 
in  the  vegetable  and  animal  king- 
doms, .  .  .  314 
Circulation  of  the  blood,  cristalliza- 

tion  of  salts,  .  .  314 

How  opake  objects  are  represented,  314 
Compound  Microscope  described,  314 
Its  Magnifying  power,  how  estima- 
ted, ...  315 
Shape  of  the  tube,  .  .  315 
Field  glass,  .  .  316 
Portable  Camera  Obscura,  described,316 

CHAPTER  VI. 

TELESCOPES. 

Telescope  defined,       .  .  317 

Its  lending  principle  enunciated,        317 
Astronomical  Telescope  described,    318 
Its  analogy  to  the  compound  micro- 
scope, .  319 
Difficulties  in  the  construction  of  the 

Telescope,    .  .  320 

Spherical  aberration,  how  corrected,  320 
Chromatic  aberration,  do.  .  323 

Dispersion  defined,     .  .  323 

Dispersive  power  of  different  bodies,  324 
How  the  Telescope  is  rendered 

achromatic,  .  .  324 

Perfection  of  the  Achromatic  Tele- 
scope, .  .  .  325 
Use  of  a  large  aperture,  .  326 
Want  of  field,  how  obviated,  327 
Imperfections  of  glass — facts,  327 
How  far  the  difficulties  have  been 

overcome,     .  .  .  328 

Barlow's  fluid  object  glasses,  328 

Their  advantages,        .  .  329 

Day  Telescope,  described,      .  329 

Mode  of  adjusting  the  eye  tube,  330 
Reflecting  Telescope  described,  331 
Advantages  and  disadvantages  of  the 

reflecting  Telescope,  .  332 

HerscheFs  great  Telescope  describ- 
ed,   .  .  .  .  332 


FART    I. MECHANICS. 

CHAPTER  1. 

PRELIMINARY  PRINCIPLES. 

1.  NATURAL  PHILOSOPHY  is  the  science  which  treats  of  the  Laws 
of  the,  material  world. 

The  term  Law,  as  here  used,  signifies  the  mode  in  which  the  pow- 
ers of  nature  act.  Laws  are  general  truths,  comprehending  a  great 
number  of  subordinate  truths. 

Natural  Philosophy,  is  divided  into  Mechanics,  Electricity,  Mag- 
netism, and  Optics. 

2.  MECHANICS  is  that  branch  of  Natural  Philosophy,  which 
treats  of  the  equilibrium  and  motion  of  bodies.*     This  definition  re- 
fers to  Mechanics  as  a  science;  the  principles  of  the  science  applied 
to  the  purposes  of  life,  as  in  the  construction  of  machinery,  consti- 
tute Practical  Mechanics. 

Body,  is  any  collection  of  matter  existing  in  a  separate  form. 
The  word  particle  is  much  used  in  writings  on  physical  subjects. 
In  Natural  Philosophy,  we  mean  by  particles,  the  smallest  parts  into 
which  a  body  may  be  supposed  to  be  divided  by  mechanical  means, 
without  any  reference  to  the  different  elements  of  which  such  parti- 
cles may  be  composed.  Inquiries  of  the  latter  kind  belong  to  chem- 
istry ;  and,  in  general,  we  recognize  no  distinctions  among  the  diffe- 
rent kinds  of  matter  which  constitute  various  bodies,  and  classes  of  bo- 
dies, (except  what  relates  to  the  states  of  solid  and  fluid,)  leaving  to 
chemistry  all  inquiries  respecting  the  composition  of  bodies,  and  the 
changes  of  nature  which  bodies  undergo  by  their  action  on  each 

other. 


*  That  is,  of  bodies  in  a  state  of  rest  or  motion,  and  of  the  forces  that 
keep  them  in  these  states  respectively. 

1 


3  MECHANICS. 

3.  Force  is  any  cause  which  moves  or  tends  to  move  a  body,  or 
which  changes  or  tends  to  change  its  motion.     Thus  the  elastic  pow- 
er of  steam  in  propelling  a  boat,  the  action  of  the  wind  upon  a  sail, 
of  a  weight  upon  a  clock,  and  of  an  animal  in  dragging  a  carriage,  are 
severally  examples  of  forces  in  actual  operation. 

That  part  of  Mechanics  which  relates  to  the  action  of  forces  pro- 
ducing equilibrium  or  rest  in  bodies,  is  called  Statics  ;  that  which  re- 
lates to  the  action  of  forces  producing  motion,  is  called  Dynamics. 

4.  The  laws  of  equilibrium  and  motion  undergo  certain  modifica- 
tions in  consequence  of  the  peculiar  properties  of  fluids.     Hence, 
that  branch  of  Mechanics  which  treats  of  the  equilibrium  and  mo- 
tion of  fluids  in  the  form  of  water,  is  called  Hydrostatics  ;  and  that 
which  treats  of  the  equilibrium  and  motion  of  fluids  in  the  form  of 
air,  is  called  Pneumatics. 

5.  The  two  essential  properties  of  matter,  both  of  which  are  in- 
separable from  it,  are  extension  and  impenetrability.     Extension,  in 
the  three  dimensions  of  length,  breadth,  and  thickness,  belongs  to 
matter  under  all  circumstances  ;  and  impenetrability,  or  the  property 
of  excluding  all  other  matter  from  the  space  which  it  occupies,  ap- 
pertains alike  to  the  largest  body  and  to  the  smallest  particle,  and 
to  bodies  under*  every  form,  solid,  fluid,  and  aeriform.     In  Geome- 
try, we  conceive  figures  to  possess  extension  only  without  solidity ; 
or  to  occupy  space  without  excluding  other  bodies  from  it;  but  in 
Mechanics,  we  take  objects  as  they  occur  in  nature,  viz.  not  only 
extended  but  impenetrable.     Thus,  in  the  demonstrations  of  geome- 
try, a  sphere  is  represented  as  existing  in  the  midst  of  a  cylinder, 
both  bodies  being  supposed,  for  the  sake  of  comparing  their  relations 
with  one  another,  to  occupy  the  same  space ;  but  when  we  seem  to 
penetrate  matter,  as  in  driving  a  nail  into  wood,   the  nail  does  not 
penetrate  the  wood,  it  displaces  it ;  and  the  same  is  the  case  when  a 
body  is  introduced  into  water  or  air. 

6.  Beside  the  two  essential  properties  of  matter,  extension  and 
impenetrability,  there  are  various  other  properties  which  are  not 
considered  as  essential  to  the  very  existence  of  matter,  since  bodies 
might  be  conceived  to  exist  without  them,  although  some  of  them 
are  in  fact  always  present.     Of  these,  two  are  intimately  connect- 


PRELIMINARY    PRINCIPLES.  O 

ed  with   the  phenomena  and  laws  of  motion :  they  are  Gravity  and 
Inertia. 

GRAVITY  is  that  property,  by  which  all  terrestrial  bodies  tend 
towards  the  center  of  the  earth.  It  is  in  this  sense  that  gravity  is 
understood  as  a  force  in  Mechanics.  But  in  order  to  give  the  learn- 
er correct  views  of  this  important  subject,  we  subjoin  a  few  other 
particulars  respecting  it. 

7.  Gravity  is  a  property  of  matter,  universally;  and  the  force  of 
gravity  in  any  body,  is  proportioned  to  its  QUANTITY  OF  MATTER. 

4 

Gravity  extends  to  all  bodies  in  the  universe,  from  the  smallest  to 
the  greatest ;  but  the  consideration  of  the  subject,  in  this  extent,  be- 
longs to  astronomy.  We  at  present  contemplate  gravity  only  as  it 
affects  terrestrial  bodies.  By  it  all  bodies  are  drawn  towards  the 
center  of  the  earth,  not  because  there  is  any  peculiar  property  or 
power  in  the  center,  but  because,  the  earth  being  a  sphere,  the  ag- 
gregate effect  of  the  attractions  exerted  .by  all  its  parts  upon  any 
body  exterior  to  it,  is  such  as  to  direct  the  body  towards  the  center. 
This  property  discovers  itself,  not  only  in  the  motion  of  falling  bod- 
ies, but  in  the  pressure  exerted  by  one  portion  of  matter  upon  anoth- 
er which  sustains  it ;  and  bodies  descending  freely  under  its  influ- 
ence, whatever  be  their  figure,  dimensions,  or  texture,  are  all  equal- 
ly accelerated,  in  a  direction  perpendicular  to  the  horizon.  The 
apparent  inequality  of  the  action  of  gravity  upon  different  species  of 
matter  near  the  surface  of  the  earth,  arises  entirely  from  the  resist- 
ance which  they  meet  with  in  their  passage  through  the  air.  When 
this  resistance  is  removed,  (as  it  may  be  done  by  means  of  an  instru- 
ment called  the  Air  Pump,  to  be  described  hereafter,)  no  such  ine- 
quality is  perceived ;  but  a  guinea,  a  feather,  and  the  smallest  par- 
ticle of  matter,  if  let  fall  together,  from  the  same  height,  will  reach 
the  plane  exactly  at  the  same  instant. 

8.  The  attraction  of  gravitation  is  RECIPROCAL,  or  every  body  at- 
tracts every  other  precisely  as  much  as  it  is  attracted  by  it. 

The  sun  has  about  a  million  times  as  much  matter  as  the  earth, 
yet  the  earth  attracts  the  sun  just  as  much  as  the  sun  does  the  earth. 
Nor  is  this  doctrine  inconsistent  with  that  asserted  in  article  7,  name- 


MECHANICS. 

]y,  that  the  force  of  gravity  in  a  body  is  proportioned  to  the  quanti- 
ty of  matter ;  for  although  the  sun  by  containing  a  million  times  as 
much  matter  as  the  earth,  exerts  a  force  a  million  times  as  great  as 
it  would  do  were  it  of  the  same  weight  with  the  earth,  yet  it  also,  on 
the  same  account,  is  capable  of  receiving  from  the  earth  a  million 
times  as  much;  and  what  the  sum  gains  by  its  greater  power  of  im- 
parting, the  earth  gains  by  the  sun's  greater  power  of  receiving. 

The  weight  of  a  body  is  the  force  it  exerts  in  consequence  of  its 
gravity,  and  is  measured  by  its  mechanical  effects,  such  as  bending  a 
spring,  or  turning  a  balance ;  or  it  is  measured  by  the  force  which 
it  takes  to  hold  a  body  back,  so  as  to  keep  it  from  falling.  The  force 
thus  exerted  by  a  given  mass  of  matter,  (as  a  cubic  foot  of  water,) 
being  taken  as  the  standard,  called  1000,  and  accurately  counter- 
poised in  a  balance,  by  some  substance  easily  susceptible  of  division, 
as  a  mass  of  lead,  for  example,  multiples  or  aliquot  parts  of  this 
standard  weight  afford  the  means  of  estimating  the  weights  of  all 
other  bodies.  Hence,  weights  are  nothing  more  than  measures  of 
the  force  of  gravity  in  different  bodies ;  but  since  the  force  of  gravi- 
ty is  proportioned  to  the  quantity  of  matter,  (Art.  7.)  weights  are 
also  measures  of  the  comparative  quantities  of  matter  in  different 
bodies. 

9.  Gravity  at  different  distances  from  the  earthy  varies  inversely  as 
the  SQUARE  OF  THE  DISTANCE  from  its  center. 

The  meaning  of  this  proposition  is,  first,  that  as  the  distance  from 
the  center  of  the  earth  increases,  the  force  of  gravity  diminishes ; 
and  secondly,  that  the  degree  of  diminution,  is  not  simply  proportion- 
al to  the  increase  of  distance,  so  as  to  be  one  half  at  double  the  dis- 
tance, and  one  third  at  three  times  the  distance,  but  it  is  proportion- 
ed to  the  square  of  the  distance,  so  that  at  twice  the  distance  it  is 
only  one  fourth  as  great,  at  three  times  the  distance,  only  one  ninth, 
and  at  a  hundred  times  the  distance,  only  one  ten  thousandth  part 
as  great.  ,-The  weight  of  a  body,  therefore,  will  vary  at  different 
heights  above  the  earth's  surface.  Thus  at  the  height  of  4000  miles, 
(which  is  about  twice  as  far  from  the  center  of  the  earth  as  bodies 
on  the  surface  are,)  a  body  would  weigh  only  half  as  much  as  at  the 
earth ;  and  the  moon,  being  about  60  times  as  far  from  the  center 


PRELIMINARY    PRINCIPLES.  O 

of  the  earth,  as  the  distance  from  that  center  to  the  surface,  the  at- 
traction of  the  earth  upon  the  moon  is  the  square  of  sixty,  that  is, 
3600  times  less  than  upon  bodies  near  the  earth ;  and,  consequently, 
very  heavy  bodies  would  become  very  light,  if  carried  to  such  a  dis- 
tance from  the  earth.  For  example,  a  cart  load  weighing  a  ton, 
would  if  lifted  to  such  a  height  as  the  moon,  weigh  less  than  ten 
ounces ;  and  a  man  of  the  largest  size,  whose  weight  was  four  hun- 
dred pounds,  would  under  such  circumstances,  weigh  less  thafti  two 
ounces.  But  the  heights  at  which  experiments  are  commonly  made 
upon  the  weights  of  bodies,  are  so  small  in  comparison  with  the  ra- 
dius of  the  earth,  that  the  loss  of  weight,  at  different  elevations,  is 
hardly  perceptible.  At  the  height  of  half  a  mile,  the  loss  could  not 
amount  to  more  than  T^ ^th  part  of  the  weight  at  the  general  level 
of  the  earth,  so  that  a  ton  of  lead  would  lose  only  about  nine  oun- 
ces, by  being  weighed  on  the  top  of  a  mountain  half  a  mile  high ; 
but  at  such  an  elevation  as  the  top  of  Chimborazo,  (which  is  nearly 
four  miles  high,)  the  diminution  of  weight  would  be  material,  being, 
in  a  ton,  about  four  pounds  and  nine  ounces.  For,  since  the  weights 
are  inversely  as  the  square  of  the  distances  from  the  center  of  the 
earth, 

4004 3  t  4000 3 :  :2240lbs.  :  22351bs.  7  oz. 

That  is,  a  ton  of  lead  would  weigh  on  the  top  of  Chimborazo  2235 
pounds  and  7  ounces,  and  of  course  would  lose  4  pounds  and  9 
ounces.  Hence,  standard  weights  are  adjusted  at  the  level  of  the  sea. 

10.  A  body  situated  within  a  hollow  sphere,  would  remain  at  rest 
in  any  part  of  the  void. 

Were  the  earth  a  hollow  shell,  with  a  crust  more  or  less  thick,  a 
ball  introduced  into  any  part  of  the  empty  space,  would  remain  per- 
fectly at  rest,  and  not  fall  either  way.  Were  the  ball  placed  in  the 
center,  it  is  easy  to  see  that  this  would  be  the  case,  since  it  would  be 
attracted  equally  on  all  sides ;  but  were  it  placed  out  of  the  center, 
and  much  nearer  to  one  side  than  to  the  other,  it  would  still  remain 
at  rest ;  for  while  the  nearer  portions  of  the  crust  would  attract  it 
more  than  the  remoter  portions,  there  would  be  so  much  more  matter 
on  the  side  of  the  latter,  as  to  counterbalance  the  advantage  which 
the  former  derived  from  its  greater  proximity. 


MECHANICS. 


Thus  in  Fig.  1.  if  the  space  be- 
tween the  two  concentric  circles  repre- 
sents the  supposed  crust  of  the  earth, 
and  a  body  were  situated  in  the  void 
at  P,  it  would  be  attracted  as  much 
more  on  the  left  of  the  line  C  D,  on 
account  of  its  being  nearer  to  the  mat- 
ter on  that  side,  as  it  would  be  on  the 
right  of  the  same  line  in  consequence 
of  the  greater  quantity  of  matter  in 
that  direction.  It  would  therefore  remain  at  rest  between  equal 
forces.  If  therefore,  a  man  were  let  down  by  a  rope  through  a  hole 
which  penetrated  the  crust,  the  force  required  to  support  him,  (in 
other  words,  his  weight]  would  grow  continually  less  and  less  until  he 
reached  the  void,  when  it  would  be  nothing. 

1 1 .  The  force  of  gravity  below  the  earth's  surface  is,  at  different 
distances  from  the  center,  directly  proportioned  to  those  distances. 

Since  the  force  of  gravity,  acting  on  bodies  exterior  to  the  earth, 
increases  rapidly  as  they  approach  the  earth,  some  have  erroneously 
supposed  that  if  a  body  could  be  let  down  through  a  pit  towards  the 
center  of  the  earth,  its  weight  would  be  greatly  augmented ;  but,  so 
far  is  this  from  the  fact,  that  were  a  body  thus  to  descend  into  the 
earth,  its  weight  would  be  continually  diminished  until  it  reached  the 
center  where  it  would  be  nothing.  This  will  be  plain,  if  it  be  con- 
sidered, that  weight  is  nothing  .more  than  the  measure  of  the  force 
of  attraction  (Art.  9.) ;  that  a  body  when  placed  at  the  center  of 
the  earth  would  be  attracted  equally  in  all  directions ;  and  that,  at 
any  point  above  the  center,  there  would  be  matter  exterior  to  it  which, 
by  its  attraction,  would  draw  it  back,  and  counteract  its  tendency  to 
descend,  and  of  course  detract  so  much  from  its  weight. 

12.  INERTIA  is  a  property  of  matter  by  which  it  resists  any  change 
of  stafyj  whether  of  rest  or  motion. 

The  inertia  of  a  body  at  rest,  is  the  resistance  to  be  overcome  to 
bring  it  to  a  given  velocity ;  or,  in  common  language,  "  to  start  it ;" 
and  the  inertia  of  a  body  in  motion,  is  the  resistance  it  makes  to 


MOTION    AND    FORCE.  ' 

being  stopped,  after  the  moving  force  is  withdrawn.  Thus  the  iner- 
tia of  a  steam  boat,  while  getting  under  weigh,  requires  a  great  ex- 
penditure of  force  to  bring  the  boat  to  its  final  velocity  ;  but  its  in- 
ertia carries  it  still  forward  after  the  engine  is  stopped.  Since  every 
particle  is  endued  with  this  property,  the  inertia  of  a  body  is  propor- 
tional to  its  quantity  of  matter,  and  of  course  to  its  weight. 


CHAPTER  II. 

OF  MOTION  AND  FORCE. 

13.  Motion  and  rest  are  accidental  states  of  bodies,  nor  is  a  body 
naturally  prone  to  one  state,  more  than  to  the  other.     If  it  is  found 
at  rest,  it  is  because  it  is  kept  at  rest  by  opposite  and  equal  forces ; 
and  if  it  is  found  in  motion,  it  is  because  it  has  been  put  in  motion  by 
some  force  extrinsic  to  itself.     The  resistances  to  motion  which  ex- 
ist near  the  surface  of  the  earth,  particularly  gravity,  create  a  seem- 
ing tendency  to  a  state  of  rest ;  but  in  reality  rest  is  no  more  the  nat- 
ural state  of  bodies  than  motion  is. 

14.  Motion  is  distinguished  into  absolute  and  relative. 

Absolute  motion,  is  a  change  of  place  with  respect  to  any  fix- 
ed point :  relative  motion,  is  a  change  of  place  in  bodies  with  res- 
pect to  each  other.  When  a  man  walks  towards  the  stern  of  a  ship, 
he  is  in  motion  with  respect  to  the  ship,  but  may  be  at  rest  with  respect 
to  the  shore.  When  a  balloon,  carried  along  by  the  wind,  attains  the 
same  velocity  as  the  wind,  it  is  relatively  at  rest,  and  appears  to  the 
aeronaut  to  be  in  a  perfect  calm,  though  it  may  be  actually  moving 
sixty  miles  an  hour.  Since  the  earth,  in  its  annual  revolution  round 
the  sun,  is  moving  eastward  at  the  rate  of  90,000  feet  per  second, 
were  a  cannon  ball,  at  a  certain  time  of  day,  fired  eastward  at  the 
rate  of  2000  feet  per  second,  the  only  effect  would  be  to  add  2000 
feet  to  the  velocity  which  the  ball  had  before  in  common  with  the 
earth ;  and  were  it  fired  westward,  the  effect  would  be  merely  to  stop 
2000  out  of  90,000  parts  of  its  previous  motion,  while  the  cannon 

-  would  proceed  onwards  leaving  it  behind.  Did  not  the  atmosphere 
partake  of  the  diurnal  motion  of  the  earth,  but  were  it  to  remain  at 
rest  with  respect  to  this  motion,  the  progress  of  any  place  to  the  east- 


MECHANICS. 

% 

ward,  would  cause  a  relative  motion  of  the  air,  or  a  wind  westward, 
which  would  blow  with  a  violence  far  surpassing  that  of  the  most  ter- 
rible hurricanes. 

15.  .Apparent  motion,  as  distinguished  from  relative,  is  that  in 
which  the  moving  body  is  quiescent,    and  the  motion  is  owing  to  a 
real  motion  in  the  spectator.     Thus  the  backward  motion  of  the 
trees  to  one  riding  rapidly,  the  receding  of  the  shore  to  one  who  is 
sailing  from  it  with  a  fair  wind,  and  the  diurnal  motion  of  the  heav- 
enly bodies  from    east  to  west,  in  consequence  of  the  revolution  of 
the  spectator  in  an  opposite  direction  :  these  are  severally  examples 
of  apparent  motion.     It  is  often  a  very  difficult  problem  to  deduce 
the  real  from  the  apparent  motion.     While  a  planet,  as  Venus,  is  re- 
volving about  the  sun  in  an  orbit  nearly  circular,  its  motions,  as  seen 
from  the  earth,  are  extremely  irregular.     The  planet  moves  for  a 
few  weeks  or  months  eastward,  then  becomes  stationary,  and  finally 
returns  westward   again.     To  make  all  these  apparent  irregularities 
consistent  with  the  real  motions,  has  been  a  perplexing  problem  in  as- 
tronomy.    We  can  sometimes  decide  that  a  given  motion  is  real,  be- 
cause we  observe  a  cause  in  operation  which  is  competent  to  produce 
it.     The  impulse  of  the  wind,  or  the  direction  of  the  current,  will 
satisfactorily  account  for  a  ship's  receding  from  a  given  object,  while 
no  cause  appears  why  the  object  should  recede  from  the  ship.     The 
revojution  of  the  earth  on  its  axis,  is  competent  to  explain  the  appar- 
ent revolution  of  the  heavens,  while  we  can  find  no  cause  for  their 
actual  revolution.     The  effects  also  of  a  given  motion,  enable  us  to 
decide  whether  it  is  real  or  apparent.     Thus,  a  constant  tendency  to 
move  in  a  straight  line,  is  characteristic  of  real  motion. 

16.  There   are  three  particulars  which  are  concerned   in  all  the 
phenomena  of  motion  ;  namely,  the  space  over  which  a  body  moves, 
the  time  of  its  motion,  and  the  velocity  with  which  it  moves.     If  the 
motion  of  a  body  be   such,   that  it  describes  equal  spaces  in  equal 
successive  parts  of  time;  then  it  is  said  to  move  with  uniform  ve- 
locity.^   Thus  when  a  ball  rolls  just  as  far  the  second  second  as  the 
first,  and  the  third  as  the  second,  its  velocity  is  uniform.     When 
the  spaces  described  in  equal  successive   parts  of  fime  continually 
increase,  it  is  said  to  move  with  an  accelerated  velocity ;  and  with  a 
retarded  velocity,  when  those  spaces  continually  decrease.     If  its 


MOTION    AND    FORCE. 

motion  be  so  regulated,  that  it  receives  equal  increments  of  velocity 
in  equal  successive  parts  of  time,  then  it  is  said  to  be  uniformly 
accelerated;  and  uniformly  retarded,  if  the  body  suffers  equal  decre- 
ments of  velocity  in  those  equal  portions  of  time. 

The  leading  principles  of  Uniform  Motion,  are  comprehended  in 
the  three  following  propositions,  which  are  to  be  treasured  up  in  the 
memory. 

17.  I.   The  SPACE  equals  the  product  of  the  time  multiplied  into 
the  velocity.* — Thus,  a  body  moving  at  the  rate  of  40  feet  per  second 
for  10  seconds,  would  evidently  pass  over  a  space  equal  to  ten  times 
40,  that  is  400  feet. 

18.  II.    The  TIME  equals  the  space  divided  by  the  velocity. — If, 
for  example,  a  body  has  passed  over  400  feet  at  the  rate  of  10  feet 
per  second,  then  10  :  1":  :400  :  4TY=40  seconds. 

19.  HI.   The  VELOCITY  equals  the  space  divided  by  the  time. 
Thus,  if  a  body  has  passed  over  400  feet  in   10  seconds,  it  must 
have  proceeded  at  the  rate  of  40  feet  per  second  ;  for, 

10"  :  400  ::i" :  4Tv>=40. 

Hence,  in  uniform  motions,  if  any  two  of  the  three  particulars, 
space,  time  and  velocity,  be  given,  the  other  may  be  found.  This 
may  be  illustrated  by  a  few  examples. 

Examples. 

20.  Ex.  1.  If  a  body  moves  uniformly  9  seconds  with  a  velocity 
of  17  feet  per  second,  through  what  space  will  it  pass  ? 

According  to  Proposition  I.  the  space  is  equal  to  the  product 
of  the  time  and  velocity;  therefore  9x17=153  feet. 

Ex.  2.  The  space  described  by  a  body  is  540  feet ;  the  velocity 
with  which  it  moves  is  6  feet  per  second  ;  what  will  be  the  time  of 
its  motion  ? 


*  The  young  learner  is  apt  to  be  puzzled  with  such  abstract  ex- 
pressions as  time  multiplied  into  velocity ;  but  it  may  be  observed, 
that  by  velocity  is  meant  nothing  more  than  the  space  passed  over 
in  one  second ;  which  may  evidently  be  so  multiplied  as  to  equal 
another  space. 

2 


10  MECHANICS. 

By  Prop.  II.  the  time  equals  the  space  divided  by  the  velocity ; 
therefore  5|0  — 90"  Ans. 

Ex.  3.  A  body  describes  560  feet  in  9  seconds  :  what  is  its 
velocity  ? 

By  Prop.  III.  the  velocity  equals  the  space  divided  by  the  time ; 
hence,  5£°— 62f  feet  per  second,  Ans. 

Questions  on  Uniform  Motions. 

21.  Ex.  1.  A  bird  of  passage  was  observed  to  fly  with  a  uniform 
velocity  of  15  feet  per  second  :  over  what  Space  would  she  pass  in  24 
hours?  Ans.  245T5T  miles. 

2.  A  lame  man  set  out  to  travel  round  the  world.     He  could  walk 
but  one  mile  an  hour  for  eight  hours  out  of  the  twenty  four.     Pro- 
vided he  could  go  forward,  without  impediment,  on  the  circumfer- 
ence of  a  great  circle  of  the  globe,  which  is  25,000  miles  round,  what 
Time  would  he  require  to  complete  the  journey  ?  Ans.  8  years  and 
205  days. 

3.  A  wind  blows  uniformly  from  the  equator  to  the  pole  (say 
6000  miles)  in  ten  days  :  what  is  its  Velocity  per  hour  ?     Ans.  25 
miles. 

Momentum  and  Force. 

22.  The  MOMENTUM  of  a  body  is  its  quantity  of  motion,  and  is 
proportioned  to  the  product  of  its  quantity  of  matter  and  velocity. 

If  two  balls,  equal  in  weight,  be  rolled  with  the  same  velocity,  it 
is  evident  that  they  will  together  have  twice  as  much  motion  as 
either  of  them  alone.  Also,  ten  balls,  in  like  circumstances,  would 
have  ten  times  as  much  motion  as  one  ball.  Nor  would  it  make  any 
difference,  as  to  the  amount  of  motion,  whether  they  moved  sepa- 
rately, or  were  united  in  one  mass.  With  a  given  velocity,  therefore, 
the  momentum  is  proportioned  to  the  quantity  of  matter.  But  the 
same  balls,  moving  with  twice  or  thrioe  as  great  velocity -as  before, 
would  have  twice  or  thrice  as  much  motion :  that  is,  the  whole 
amount  of  motion,  or  the  momentum,  is  found  by  multiplying  the  . 
quantity  of  matter  by  the  velocity.  Thus  a  single  ball  mdy  have  as 
much  momentum  as  one  hundred  similar  balls,  if  it  moves  a  hundred 
times  as  fast  as  they  do ;  or,  in  general,  a  small  mass  of  matter  may 
have  the  same  momentum  with  a  large  mass,  if  its  velocity  be  as 
much  greater  as  its  weight  is  less. 


MOTION    AND    FORCE.  11 

« 

23.  FORCE  is  any  cause  which  moves  or  tends  to  move  a  body,  or 
which  changes  or  tends  to  change  its  motion.     (See  Art.  3.) 

The  -measure  of  a  force,  is  the  change  of  motion  which  it  produ- 
ces ;  and  the  momentum  of  a  body  is  determined  by  the  force  re- 
quired to  stop  it.  Momentum  is  estimated  in  pounds  weight,  a 
weight  just  sufficient  to  balance  it  being  supposed  to  act  against  it  by 
means  of  a  cord  passing  over  a  pulley.  Thus  a  cannon  ball  may  be 
said  to  move  with  a  momentum  of  1,000  pounds,  because,  were  a 
scale  loaded  with  this  weight  and  attached  to  one  end  of  a  cord, 
while  the  other  end  was  attached  to  the  ball,  (the  cord  passing  over 
a  pulley,)  the  ball  and  the  weight  would  exactly  balance  one  anoth- 
er, and  the  ball  would  be  said  to  move  with  a  momentum  of  1000 
pounds.  The  weight,  moreover,  would  be  a  /orce,  acting  against 
the  ball,  tending  to  move  it  in  the  opposite  direction. 

Examples. 

24.  Ex.  1.  A  weighs  50  pounds  and  moves  af  the  rate  of  60  feet 
in  a  second  :  B  weighs  300  pounds  and  moves  at  the  rate  of  10  feet 
per  second :  How  are  their  momenta?  Ans.  equal;  for  50x60= 
300x10. 

Ex.  2.  A  weighs  7  Ibs.  and  is  moving  with  a  velocity  of  9  feet  in 
a  second ;  B  weighs  5  Ibs.  and  moves  with  a  velocity  of  1 1  feet  in  a 
second :  What  are  their  comparative  momenta  ?  Momentum  of  A 
:  momentum  of  B::  7x9  :  5x11;  that  is,  63  :  55  Ans. 

Ex.  3.  Suppose  the  battering  ram  of  Vespasian,  weighed  10,000 
pounds,  and  was  propelled  with  a  velocity  of  20  feet  per  second,  and 
that  this  force  was  found  sufficient  to  demolish  the  walls  of  Jerusa- 
lem. With  what  velocity  must  a  32  pound  ball  move  to  do  the  same 
execution  ? 

The  ball,  in  order  to  do  the  same  execution  as  the  battering  ram, 
must  have  the  same  force,  that  is  the  same  momentum.  Now  the  mo- 
mentum ofthe  battering  ram  is  10,000x20=200,000;  and  this  di- 
vided by  32  gives  6,250  for  the  number  of  feet  per  second  the  ball 
must  move  in  order  to  have  a  momentum  of  200,000  pounds. 

Ex.  4.  Suppose  a  grain  of  light,  moving  at  the  rate  of  195,000 
miles  per  second,  should  impinge  directly  against  a  mass  of  ice,  float- 
ing at  the  rate  of  one  foot  per  second  :  what  weight  of  ice  would  the 
light  stop?  Ans.  147085.7042 Ibs;  or  more  than  65  tons. 


12  MECHANICS. 

Ex.  5.  The  earth  being  8000  miles  in  diameter,  if  a  ball  of  the  same 
density  with  the  earth,  T^th  of  a  mile  in  diameter,  were  placed  at 
the  distance  of  ^th  of  a  mile  above  the  earth ;  what  space  would 
the  earth  move  through  to  meet  it?  Ans.  j o^o-o-lo  o^o  otn  mcn-  nearly.* 


CHAPTER  III. 

OF  THE  LAWS  OF  MOTION. 

25.  THERE  are  three  fundamental  principles  of  motion,  of  most 
extensive  application  in  Mechanics,  which  are  called  the  Laws  of  Mo- 
tion.    They  are  very  rejnarkable  examples  of  a  happy  generalization ; 
but  their  very  comprehensiveness  renders  them  difficult  to  be  under- 
stood by  the  young  learner;  nor  can  they  be  thoroughly  mastered, 
in  all  their  relations,  until  after  considerable  proficiency  is  made  in 
the  science  of  Mechanics.     We  shall  endeavor  to  make  them  as 
plain  as  possible  by  a  variety  of  illustrations. 

26.  FIRST  LAW. — Jl  body  continues  always  in  a  state  of  rest,  or 
of  uniform  motion  in  a  right  line,  till  by  some  external  force,  it  is 
made  to  change  its  state. 

This  law  contains  the  doctrine  of  Inertia,  expressed  in  four  particu- 
lars. First,  that  unless  put  in  motion  by  some  external  force,  a  body 
always  remains  at  rest ;  secondly,  that  when  once  in  motion,  it  con- 
tinues always  in  motion  unless  stopped  by  some  force  ;  thirdly,  that 
the  motion  arising  from  inertia,  is  always  uniform ;  and,  fourthly,  that 
this  motion  is  in  right  lines. 

27.  That  a  body  at  rest  will  continue  at  rest,  is  a  consequence 
immediately  arising  from  the  inertia  of  matter.    (Art.  12.)     That  a 


*  In  order  to  solve  this  question,  the  learner  must  bear  in  mind, 
ihat  the  two  bodies  would  approach  each  other  with  equal  momenta 
(Art.  8.) ;  but  that  the  space  over  which  the  earth  would  pass,  would 
be  as  much  less  than  that  of  the  smaller  body,  as  its  quantity  of  mat- 
ter was  greater ;  and  that  the  quantities  of  matter  in  spheres,  are  pro- 
portioned to  the  cubes  of  their  diameters. 


LAWS    OF    MOTION.  13 

body  in  motion  will  continue  to  proceed  uniformly  along  the  right  line 
in  which  it  began  to  move,  until  it  is  acted  upon  by  some  external 
force,  is  inferred  from  the  fact,  that  any  deviation  from  uniform^  rec- 
tilinear motion,  in  a  moving  body,  is  observed  to  be  owing  to  some 
external  force;  and  that  such  deviation  is  diminished  as  such  exter- 
nal force  is  withdrawn  :  hence,  were  it  entirely  withdrawn,  the  mo- 
tion of  the  body  would  become  altogether  uniform,  rectilinear,  and 
perpetual.  We  may  see  approximations  to  such  a  state,  in  a  ball 
rolled  successively  on  'the  earth,  on  a  floor,  and  on  smooth  ice. 
Although,  on  account  of  the  numerous  impediments  to  motion  which 
exist  at  the  surface  of  the  earth,  bodies  are  unable  to  maintain  for 
any  considerable  time,  the  motion  they  have  acquired,  yet  we  see 
the  first  law  of  motion,  so  far  as  it  respects  the  tendency  of  bodies 
to  persevere  in  motion,  fully  confirmed  in  the  continued  and  unalter- 
ed revolution  of  the  heavenly  bodies.  These  are  impelled  by  no 
renewed  forces,  but  revolve  from  age  to  age  in  an  undeviating  course, 
simply  because  they  meet  with  no  impediments. 

28.  We  may  see  various  exemplifications  of  this  law,  in  the  oc- 
currences that  daily  present  themselves  to  our  observation.     And 
first,  with  respect  to  bodies  at  rest.     Their  tendency  to  remain  at 
rest  is  seen,  when  a  horse  starts  suddenly  forward,  and  his  rider  is 
thrown  backward.     In  consequence  of  the  inertia  of  matter,  before 
a  body  can  be  brought  to  the  required  velocity,  this  velocity  must 
be  impressed  on  every  particle  of  matter  it  contains.     Hence  the 
more  numerous  its  particles,  the  greater  is  the  resistance  from  iner- 
tia ;  that  is  the  resistance  is  proportioned  to  the  quantity  of  matter. 
A  vast  weight  may  be  moved  on  a  horizontal  rail  way  by  a  compara- 
tively small  force,  provided  it  can  be  got  into  motion,  with  the  re- 
quired velocity.     In  transporting  large  quantities  (eighty  tons  for  in- 
stance,) of  coal,  the  weight  is  distributed  into  a  number  of  different 
cars,  connected  together  by  a  loose  chain,  in  order  that  the  inertia 
of  the  several  parts  may  be  overcome  successively. 

29.  In  consequence  of  the  inertia  of  matter,  the  motion   applied 
to  a  body,  does  not  instantly  pervade  the  mass.     In  order  to  this, 
motion  must  be  applied  gradually,  especially  if  the  body  is  large ; 


14  MECHANICS. 

for,  if  it  is  applied  suddenly,  it  is  frequently  all  expended  on  a  part 
of  the  mass,  the  cohesion  is  overcome,  and  the  body  is  broken. 
This  explanation  may  be  applied  to  several  familiar  facts.  When  a 
team  starts  suddenly  forward  with  a  heavy  load,  the  effort  is  either 
wholly  ineffectual,  or  some  part  of  the  harness  or  tackling  gives  way. 
If  we  draw  a  heavy  weight  by  a  slender  string,  a  slow  and  steady  pull 
will  move  the  weight,  when  a  sudden  twitch  would  break  the  string 
without  starting  the  mass.  The  same  principle  applies  to  bodies  al- 
ready in  motion.  Thus,  when  a  horse  in  a  carriage  starts  suddenly 
forward,  he  may  break  loose  as  well  when  the  carriage  was  previously 
in  motion  as  when  it  was  at  rest.  The  inertia  of  a  body  is  in  fact 
the  same  whether  the  body  is  in  motion  or  at  rest,  opposing  the  same 
resistance  to  its  moving  with  increased  velocity,  as  to  its  beginning  to 
move  from  a  state  of  rest. 

30.  Several    singular  phenomena  result  from  the  same  cause, 
showing  that  time  is  necessary  in  order  that  motion  communicated  by 
impulse,  may  pervade  the  entire  mass.     A  pistol  ball,  fired  through 
a  pane  of  glass,  frequently  makes  a  smooth  well  defined  hole,  and 
does  not  fracture  the  other  parts  of  the  glass.     Here,  the  moment- 
um of  the  ball  is  communicated  to  the  particles  of  glass  immediately 
before  it.     Had  the  impulse  been  gradual,  the  same  motion  would 
have  diffused  itself  over  the  whole  pane,  and  every  part  would  have 
felt  the  shock.     A  ball  fired  through  a  board  delicately  suspended, 
causes  no  vibration  in  the  board.     A  cannon  ball,  having  very  great 
velocity,  passes  through  a  ship's  side,  and  leaves  but  a  little  mark, 
while  one  with  less  speed,  splinters  and  breaks  the  wood  to  a  con- 
siderable distance  around.     A  near  shot  thus  often  injures  a  ship  less 
than  one  from  a  greater  distance.     A  soft  substance,  as  clay  or  tal- 
low, may  be  fired  through  a  plank  before  the  motion  has  had  time  to 
diffuse  itself  through  the  contiguous  parts.     The  whole  momentum 
being  concentrated  upon  the  part  immediately  before  the  body,  the 
cohesion  of  that  part  is  destroyed. 

31.  Secondly,  let  us  consider  the  effects  of  Inertia  as  it  respects 
bodies  in  motion.     All  bodies  in  contact  with  each  other  acquire  a 
common  motion ;  as,  for  example,  a  horse  and  his  rider,  a  ferry  boat 
and  its  passengers,  a  ship  and  every  thing  within  it,  the  earth  and  all 


LAWS    OF    MOTION.  15 

things  on  its  surface.  Whenever  either  of  these  bodies  stops  sud- 
denly, the  movable  bodies  connected  with  it,  are  thrown  forward* 
Were  the  revolution  of  the  earth  on  its  axis  to  be  suddenly  arrested, 
the  most  dreadful  consequences  would  ensue ;  every  thing  movable 
on  its  surface,  as  waters,  rocks,  cities,  and  animals,  not  receiving, 
instantaneously,  this  backward  impulse,  would  fly  off  eastward,  in 
promiscuous  ruin.  Were  the  diurnal  motion  of  earth,  however,  very 
gradually  diminished,  until  it  finally  ceased,  so  that  time  should  be 
affocded  to  communicate  the  loss  of  motion  by  slow  degrees  to  the 
bodies  on  its  surface,  no  such  effects  would  take  place.  If  a  pas- 
senger leaps  from  a  carriage  in  rapid  motion,  he  will  fall  in  the  di- 
rection in  which  the  carriage  is  moving  at  the  moment  his  feet  meet 
the  ground ;  because  his  body,  on  quitting  the  vehicle,  retains,  by 
its  inertia,  the  motion  which  it  had  in  common  with  it.  When  he 
reaches  the  ground,  this  motion  is  destroyed  by  the  resistance  of  the 
ground  to  the  feet,  but  is  retained  in  the  upper  and  heavier  part  of 
the  body,  so  that  the  same  effect  is  produced  as  though  the  feet  had 
been  tripped.  Coursing  owes  all  its  interest  to  the  instinctive  con- 
sciousness of  the  nature  of  inertia,  which  seems  to  govern  the  meas- 
ures of  the  hare.  The  greyhound  is  a  comparatively  heavy  body 
moving  at  the  same  or  greater  speed  in  pursuit.  The  hare  doub- 
les, that  is,  suddenly  changes  the  direction  of  her  course,  and  turns 
back  at  an  oblique  angle  with  the  direction  in  which  she  had  been 
running.  The  greyhound,  unable  to  resist  the  tendency  of  its  body 
to  persevere  in  the  rapid  motion  it  had  acquired,  is  urged  forwards 
many  yards  before  it  is  able  to  check  its  speed  and  return  to  the 
pursuit.  Meanwhile  the  .hare  is  gaining  ground  in  the  other  direc- 
tion, so  that  the  animals  are  at  a  very  considerable  distance  asunder 
when  the  pursuit  is  recommenced.  In  this  way  a  hare,  thlough 
much  less  fleet  than  a  greyhound,  will  often  escape  it. 

32.  Thirdly,  bodies  in  consequence  of  their  inertia,  have  a  ten- 
dency to  move  over  equal  spaces  in  equal  times,  that  is,  to  move 
uniformly.  In  a  ball  rolled  on  ice,  in  a  pendulum  continuing  to  vi- 
brate after  the  moving  force  is  withdrawn,  and  in  numerous  cases 
similar  to  these,  we  observe  both  in  nature  and  art  this  tendency 
to  uniform  motion ;  but  in  all  these  cases,  the  motion  is  not  abso- 
lutely uniform,  but  is  more  or  less  retarded  by  the  resistances  en- 


16 


MECHANICS. 


countered.     A  much  nearer  approximation  to 
the  truth  is  obtained  by  means  of  an  apparatus 
called  Jltwooffs  Machine,  (Fig.  2.)     Its  con- 
struction, omitting  some  parts  not  essential  to 
the  principle,  is  as  follows.     The   triangular 
base  and  upright  pillars  (which  are  usually  of 
mahogany)  constitute  the  frame,  which  is  sur- 
mounted by  a  horizontal  table  or  plate  of  wood 
A  B,  perforated  with  several  holes.     C  is  a 
vertical  wheel,  which  by  a  contrivance  called 
friction  wheels,  (not  represented  in  the  figure,) 
is  made  to  revolve  with  the  least  possible  resist- 
ance from  friction.     D  and  E  are  two  weights 
exactly  equal,  and  connected  by  a  slender  string 
passing  over  the  wheel  C.     FG  is  a  perpen- 
dicular scale  graduated  into  inches  from  top  to 
bottom,  extending  from  0  to  60  or  70,  accord- 
ing to  the  height  of  the  machine.     H  is  a  mov- 
able ring  which  slides  up  and  down  on  the 
scale,  and  K  is  a  brass  plate  sliding  in  the  same 
manner.     There  are  also  sometimes  connect- 
ed with  the  machine,  a  pendulum,   and  such 
parts  of  a  clock  as  are  necessary  for  beating 
seconds,  in  order  that  the  time  of  each  exper- 
iment may  be  accurately  noted. 


33.  A  great  variety  of  the  principles  of 
tion,  may  be  established  by  means  of  this  apparatus,  but  we  are  at 
present  concerned  only  with  the  method  of  showing  that  a  body 
when  once  put  in  motion  continues,  by  its  inertia,  to  move  uniform- 
'ty,  after  the  moving  force  is  withdrawn.  It  is  obvious  that  the 
weights  D  and  E  balance  each  other,  and  consequently  that  the 
power  of  gravity  is  entirely  removed  from  D,  so  that  it  is  at  liberty 
to  obey  the  full  and  exclusive  influence  of  any  force  that  may  be 
applied'-to  it.  If  therefore,  an  impulse  be  given,  by  the  finger,  for 
example,  to  D  when  at  the  top  of  the  scale,  it  ought  in  conformity 
to  the  law  under  consideration  to  move  uniformly  along  down  the 
scale,  passing  over  the  same  number  of  inches  in  each  successive 
second.  Such  appears  to  be  the  fact  ;  but  in  order  to  give  a  still 


LAWS    OF    MOTION.  17 

greater  precision  to  the  experiment,  a  small  brass  bar  is  laid  on  D, 
which  communicates  motion  to  it,  accelerating  its  progress  until  it 
comes  to  the  brass  ring  H,  where  the  bar  lodges  and  the  weight 
proceeds  on  with  the  velocity  acquired.  This  velocity  is  found  to 
be  uniform ;  that  is,  the  weight  D  after  it  leaves  the  ring  passes  ac- 
curately over  the  same  number  of  inches  on  the  scale  in  each  suc- 
cessive second. 

34.  Fourthly,  moving  bodies  have  a  constant  tendency  to  move 
in  right  lines.     In  nature,  there  occur,  indeed,  but  few  examples  of 
rectilinear  motion,  but  almost  every  moving  body  describes  a  curve. 
Thus,  the  heavenly  bodies  move  in  ellipses  or  ovals ;  bodies  thrown 
into  the  air  describe  a  curve  called  a  parabola ;  or  if  their  direction 
is  so  altered  by  a  resisting  medium  that  their  path  is  no  longer  a  par- 
abola, it  is  still  changed  to  some  other  curve ;   and  a  ship  sailing 
across  the  ocean,  describes  a  curvilinear  path  on  the  surface  of  the 
earth.     The  waving  of  trees  and  plants,  the  courses  of  rivers,  the 
spouting  of  fluids,  the  motions  of  winds  and  waves,  are  likewise 
more  or  less  curvilinear.     Bodies  falling  towards  the  earth  by  grav- 
ity, present  almost  the  only  examples  we  observe  in  nature  of  a  mo- 
tion purely  rectilinear ;  and  this  is  so  only  in  appearance.     But  not- 
withstanding the  deviation  from  a  right  line,  observable  in  actual  mo- 
tions, yet  we  find  that  there  is  always  some  extraneous  cause  in  op- 
eration which  accounts  for  such  deviations. 

35.  In  consequence  of  this  tendency  of  moving  bodies  to  proceed 
in  right  lines,  when  a  body  revolves  in  a  curve,  around  some  center 
of  motion,  it  constantly  tends  to  fly  off  in  a  straight  line  which  is  a 
tangent*  to  its  orbit.     The  force  which  thus  carries  a  body  off  from 
the  center  of  motion,  is  called  the  centrifugal  force.     A  stone  from 
a  sling,  water  escaping  from  the  circumference  of  a  revolving  wheel, 
and  water  receding  from  the  center  of  a  tumbler  or  pail  when  the 
vessel  is  whirled,  are  familiar  instances  of  the  tendency  of  bodies 
when  revolving  in  circles  to  fly  off  in  straight  lines.     If  a  pail,  con- 
taining a  little  water,  be  hung  up  by  the  ears,  by  a  cord  suspended 

*  A  tangent  is  a  straight  line  which  touches  the  circumference  of  a 
circle. 

3 


18  MECHANICS. 

from  the  ceiling  of  a  room,  on  turning  the  pail  and          F|g-  3- 

.       .  .          iimimiiiiiiiiimmiiimiiiii 

twisting  up  the  cord,  and  then  suffering  it  to  untwist 

so  as  to  give  a  rapid  revolution  to  the  pail,  the  water 
will  rise  on  the  sides  of  the  vessel,  and,  if  the  motion 
be  sufficiently  rapid,  it  will  be  thrown  out  of  the  ves- 
sel in  lines  which  are  tangents  to  the  surface  of  the 
vessel.  If  a  glass  vessel  of  suitable  size  and  shape* 
be  substituted  for  the  pail,  the  experiment  is  observ- 
ed to  better  advantage.  Such  a  vessel  is  represented 
in  the  annexed  figure. 

36.  The  action  of  the  centrifugal  force  may  be  stud- 
ied still  more  advantageously  by  means  of  the  appara- 
tus called  the  Whirling  Tables.     These  consist  of  two 

small  circular  tables,  to  which  (by  means  of  a  crank)  is  communicated 
a  horizontal  revolution  around  their  centers.  Bodies  laid  on  the  Ta- 
bles in  different  ways,  are  made  to  participate  in  their  rotary  mo- 
tions, and  thus  the  laws  of  the  centrifugal  force  may  be  observed.  By 
means  of  this  apparatus,  the  following  propositions  are  established. 

37.  (1.)  The  centrifugal  force  of  bodies  revolving  in  a  given  cir- 
cle, is  proportioned  to  their  densities  or  specific  gravities.     If  quicksil- 
ver, water,  and  cork,  be  whirled  together  in  a  tub  or  vessel,  these 
bodies  arrange  themselves  in  the  inverse  order  of  their  specific 
gravities,  so  that  the  cork  will  be  at  the  least,  and  the  quicksilver  at 
the  greatest  distance  from  the  center  of  the  vessel. f 

38.  (2.)  When  bodies  revolve  in  the  same  circle  with  different 
velocities,  the  centrifugal  forces  are  proportioned  to  the  squares  of 
the  velocities.     By  doubling  the  velocity  of  a  revolving  body  its 
centrifugal  force  is  quadrupled ;  and  ten  times  a  former  velocity,  gives 
one  hundred  times  the  former  centrifugal  force.     Millstones,  revol- 
ving horizontally,  communicate  their  circular  motion  to  the  corn  that 
is  introduced  between  them,  near  the  center.     The  corn,  by  the 

*  A  large  bell  glass  receiver  belonging  to  the  air  pump,  answers 
well  for  this  purpose. 

t  This  experiment  may  be  conveniently  performed  in  the  suspen- 
ded vessel  Fig.  3. 


LAWS    OF    MOTION. 


19 


centrifugal  force  which  it  gradually  acquires,  recedes  from  the  center 
and  passes  out  at  the  circumference.  If  too  great  a  velocity  be  given 
to  millstones,  they  sometimes  burst  with  violence.  A  horse  in  swift 
motion,  on  suddenly  turning  a  corner,  throws  his  rider ;  and  a  car- 
riage turning  swiftly  is  overset  on  the  same  principle.  In  feats  of 
horsemanship,  when  the  equestrian  rides  rapidly  round  a  small  ring, 
he  inclines  his  body  inwards  in  different  degrees  according  to  the 
velocity  with  which  he  is  moving,  and  thus  counteracts  his  tendency 
to  fall  outwards  by  the  centrifugal  force. 

39.  (3.)  Hence,  when  spherical  bodies  revolve  on  their  axis,  the 
equatorial  parts  being  farther  from  their  center  of  motion,  and  conse- 
quently moving  faster  than  the  other  parts,  have  a  proportionally  greater 
centrifugal  force.  If  the  revolving  body  is  soft  so  as  to  yield,  it  is  ele- 
vated in  the  equatorial  and  depressed  in  the  polar  parts.  Thus  a  mass 
of  clay  revolving  on  a  potter's  wheel,  swells  out  in  the  central  parts 
and  becomes  flattened  at  the  two  ends.  The  earth  itself,  by  its 
figure,  which  is  an  oblate  spheroid,*  indicates  the  operation  of  this 
principle ;  and  the  planet  Saturn,  which  has  a  far  more  rapid  revo- 
lution on  its  axis,  indicates  the  same  modification  of  its  figure  in  a 
still  higher  degree,  being  strikingly  elevated  at  the  equator  and  de- 
pressed at  the  poles.  Let  the  circle  in 
Fig.  4.  represent  a  section  of  the  earth, 
A  B  being  the  axis  on  which  it  revolves. 
This  rotation  causes  the  matter,  which 
composes  the  mass  of  the  earth,  to  re- 
volve in  circles  round  the  different  points 
of  the  axis  as  centers,  at  the  various  dis- 
tances  at  which  the  component  parts  of  the 
mass  are  placed.  As  they  all  revolve 
with  the  same  angular  velocity,  they  will 
be  affected  by  the  centrifugal  forces, 
which  will  be  greater  or  less  in  propor- 
tion as  their  distances  from  the  center  are  greater  or  less.  Con- 


*  A  spheroid  differs  from  a  globe  or  sphere,  in  being  flattened  in 
one  direction  and  lengthened  in  the  other.  The  spheroid  is  oblate 
when  its  figure  is  flattened  like  an  orange,  and  prolate  when  elongated 
like  a  lemon. 


20  MECHANICS. 

sequently,  the  parts  of  the  earth  which  are  situated  about  the 
equator,  Q,  will  be  more  strongly  affected  by  centrifugal  forces  than 
those  about  the  poles  A,  B  :  the  effect  of  the  difference  has  been, 
that  the  component  matter  about  the  equator  has  actually  been  driven 
farther  from  the  center  than  that  about  the  poles,  so  that  the  figure 
of  the  earth  has  swelled  out  at  the  sides,  and  appears  proportionally 
depressed  at  the  top  and  bottom,  resembling  an  orange  in  shape. 

40.  The  centrifugal  force  of  the  earth's  rotation  also  affects  de- 
tached bodies  on  its  surface.  If  such  bodies  were  not  held  upon 
the  surface  by  the  earth's  attraction,  they  would  be  immediately  flung 
off  by  the  whirling  motion  in  which  they  participate.  The  centri- 
fugal force,  however,  really  diminishes  the  effect  of  the  earth's  attrac- 
tion on  those  bodies,  or  what  is  the  same  diminishes  their  weights. 
If  the  earth  were  not  revolving  on  its  axis,  the  weight  of  bodies  in 
all  places  equally  distant  from  the  center  would  be  the  same ;  but 
this  is  not  so  when  the  bodies,  as  they  do,  move  round  with  the  earth. 
They  acquire  from  the  centrifugal  force  a  tendency  to  fly  off  from 
the  axis ;  which  increases  with  their  distance  from  that  axis,  (Art.  39.) 
and  is  therefore  greater  the  nearer  they  are  to  the  equator,  and  less  as 
they  approach  the  pole.  But  there  is  another  reason  why  thp  centrifu- 
gal force  is  more  efficient,  in  the  opposition  which  it  occasions  to  gravi- 
ty, near  the  equator  than  near  the  poles.  This  force  does  not  act  from 
the  center  of  the  earth,  but  its  direction  is  in  a  line  perpendicular  to 
the  earth's  axis.  Thus  in  Fig.  4,  the  centrifugal  forces  act,  not  in  the 
lines  C  F,  C  F,  but  in  the  lines  O  F,  O  F,  &c.  This  force  is  there- 
fore not  directly  opposed  to  gravity,  except  on  the  equator  itself. 
On  leaving  the  equator  and  proceeding  towards  the  poles,  it  is  less 
and  less  opposed  to  gravity.  If  the  diurnal  motion  of  the  earth  around 
its  axis,  were  about  seventeen  times  faster  than  it  is,  the  centrifugal 
force  would,  at  the  equator,  be  equal  to  the  power  of  gravity,  and  all 
bodies  there  would  entirely  lose  their  weight ;  and  if  the  earth  re- 
volved,still  quicker  than  this,  they  would  all  fly  off. 

*V 
41.  The  consideration  of  centrifugal  force  proves,  that  if  a  body 

be  observed  to  move  in  a  curvilinear  path,  some  efficient  cause  must 
exist  which  prevents  it  from  flying  off,  and  which  compels  it  to  revolve 
round  the  center.  Thus  the  bodies  of  the  solar  system  are  constantly 


LAWS    OF    MOTION.  21 

impelled  or  drawn  towards  the  sun  by  a  force  which  we  denominate 
gravity.  If  this  force  did  not  act  constantly,  they  would  resume  their 
motion  in  the  right  line  in  which  they  were  originally  projected,  when 
they  were  first  launched  into  space,  and  would  continue  moving  in  it 
forever. 

42.  SECOND  LAW. — Motion,  or  change  of  motion,  is  propor- 
tional to  the  force  impressed,  and  is  produced  in  the  right  line  in  which 
that  force  acts. 

First,  motion  is  proportional  to  the  force  impressed.  This  is  very 
satisfactorily  shown  by  means  of  Atwood's  Machine.  (Fig.  2.) 
When  the  box  D  is  loaded  with  bars  of  different  weights,  (the  bars 
being  left  on  the  ring,  H,  as  in  Art.  32.)  the  box  descends  along 
the  scale,  in  consequence  of  the  motion  given  it  by  the  bar,  with  ve- 
locities exactly  proportional  to  the  weights  of  the  bars  respectively. 

43.  Secondly,  motion  is  in  the  direction  of  the  force  impressed. 
Notwithstanding  the  diversity  of  motions  to  which  eyery  terrestrial 
body  is  constantly  subject,  the  effect  of  any  force  to  produce  motion, 
is  the  same,  when  the  spectator  has  the  same  motion  with  the  body,  as 
though  that  body  were  absolutely  at  rest.     In  other  words,   all  mo- 
tions are  compounded  so  as  not  to  disturb  each  other ;  each  remain- 
ing, relatively,  the  same  as  if  there  were  no  others.    Since,  for  exam- 
ple, by  the  diurnal  motion  of  the  earth,  places  towards  the  equator 
move  faster  than  those  towards  the  poles,  if  the  foregoing  principle 
were  not  true,  the  same  forces  would  produce  different  quantities  of 
motion  in  different  latitudes ;  and  a  body  struck  in  a  direction  north 
or  south,  would  not  move  in  that  direction,  but  would  deviate  to  the 
east  or  west.  ,A  pendulum,  also,  would  vibrate  differently  accordingly 
as  it  moved  in  a  north  and  south,  or  in  an  east  and  west  direction, 
whereas  not  the  slightest  difference  of  time  can  now  be  detected.     If 
we  are  in  a  ship,  moving  equably,  any  force  which  we  can  exert  will 
produce  the  same  motion  relative  to  the  vessel,  whether  it  be  or  be 
not  in  the  direction  of  the  vessel's  motion.     If  we  stand  on  the  deck, 
supposed  to  be  level,  and  roll  a  body  along  it,  the  same  effort  will  pro- 
duce the  same  velocity  along  the  deck  whether  the  motion  be  from 
head  to  stern,  or  from  stern  to  head,  or  across  the  vessel.     Also  a 
body  dropped  from  the  top  of  the  mast  will  not  be  left  behind  by  the 
motion  of  the  ship,  but  will  fall  along  the  mast  as  it  would  if  the  mast 


22  MECHANICS. 

were  at  rest,  and  will  reach  the  foot  of  it  at  the  same  time.  If  a 
body  be  thrown  perpendicularly  upwards,  it  will  rise  directly  over 
the  hand  and  fall  perpendicularly  upon  it  again ;  and  if  it  be  thrown 
in  any  other  direction,  the  path  and  motion  relative  to  the  person  who 
throws  it  will  be  the  same  as  if  he  were  at  rest. 

44.  Since,  according  to  the  second  law  of  motion,  the  change  of 
motion  is  proportional  to  the  force  impressed,  it  follows  that  the 
smallest  force  is  capable  of  moving  the  largest  bodies.     Agreeably  to 
this  doctrine,  a  blow  with  a  hammer  upon  the  earth  ought  to  move 
it,  and  that  it  would  do  so  may  be  inferred  from  the  following  reasons. 

(1.)  We  can  conceive  the  earth  to  be  divided  into  parts  so  small, 
that  the  blow  would  produce  upon  one  of  them  even  a  sensible  mo- 
tion. Then  it  would  produce  on  two  of  the  parts  half  as  much  ve- 
locity ;  and  upon  all  the  parts  together  a  velocity  as  much  less  than 
upon  one,  as  their  number  was  greater  than  unity.  This  velocity 
might  be  appreciable  in  numbers,  although  too  small  to  be  observed 
by  the  senses. 

(2.)  Very  heavy  weights  may  be  actually  put  in  motion  by  small 
forces.  Leslie  asserts  that  a  ship  of  any  burden  may  in  calm  weather 
and  smooth  water,  be  gradually  pulled  along,  even  by  the  exertions  of 
a  boy. 

(3.)  The  repetition  of  very  small  blows,  finally  produces  sen- 
sible effects  upon  large  bodies.  The  wearing  away  of  stone  by  the 
dropping  of  water,  the  abrasion  of  marble  images  by  the  kisses  of 
pilgrims,  and  especially,  the  demolition  of  the  strongest  fortresses  by 
repeated  blows  of  the  battering  ram,  are  examples  of  the  power- 
ful effects  produced  by  small  impulses,  each  of  which  must  have 
contributed  its  share,  since  the  addition  of  any  number  of  nothings 
is  nothing  still. 

45.  THIRD  LAW. — When  bodies  act  upon  each  other,  action  and 
reaction  are  equal  and  in  opposite  directions. 

If  I  strike  one  hand  upon  the  other  at  rest,  I  perceive  no  differ- 
ence in  'the  sensations  experienced  by  each.  The  resistance  to  the 
hand  which  gives  the  blow  is  equal  to  the  impulse  given.  A  boat- 
man presses  against  the  bank  with  his  oar,  and  receives  motion  in  the 
opposite  direction,  which  being  communicated  through  him  to  the 


LAWS    OF    MOTION.  23 

boat,  makes  it  recede  from  the  shore.  He  strikes  the  water,  the 
reaction  of  which,  at  every  impulse  carries  the  boat  forward  in  the 
opposite  direction.  An  infirm  old  man  presses  the  ground  with  his 
staff,  and  thus  by  lightening  the  pressure  on  his  lower  limbs,  makes 
his  arms  perform  a  part  of  the  labor  of  walking.  A  bird  beats  the 
air  with  his  wings,  and  by  giving  a  blow  whose  reaction  is  more  than 
sufficient  to  balance  the  weight  of  his  body,  rises  with  the  difference. 
When  the  wings  are  small  and  slender,  as  those  of  the  humming  bird, 
and  disproportioned  to  the  weight  of  the  body,  the  defect  is  compen- 
sated by  more  frequent  blows,  giving  nimble  motions  suited  to  their 
short  but  swift  excursions,  while  the  long  wings  of  the  eagle  are 
equally  fitted,  by  their  less  rapid,  but  more  effectual  blows,  for  their 
distant  journeys  through  the  skies.  Hence,  propelling  and  rowing  a 
boat,  flying,  and  swimming,  are  processes  analogous  to  each  other, 
depending  on  the  principle  of  reaction. 

46.  If  a  man  stands  in  a  boat  and  pulls  upon  a  rope  which  is  fas- 
tened to  a  post  ori  the  shore,  the  force  of  the  man  is  expended  on  the 
post  in  one  direction,  and  the  post,  by  its  reaction,  draws  the  man 
in  the  opposite  direction,  namely,  towards  the  shore.     Call,  the  man 
A,  and  let  another  man  B,  take  the  place  of  the  post.     If  B  pulls 
with  a  force  just  equal  to  that  of  A,  he  will  do  nothing  more  than 
what  the  post  did  before,  and  therefore  the  two  men  together  will 
bring  the  boat  ashore  no  sooner  than  A  would  have  done  alone  in  the 
former  case.     If  A  pulls  with  more  force  than  B,  he  pulls  B  towards 
him  and  the  reaction,  or  the  force  which  carries  the  boat  ashore,  is 
the  same  as  before,  namely  the  force  of  B.     If  B  were  to  pull  with 
more  force  than  A,  he  would  pull  A  out  of  the  boat,  were  not  A  at- 
tached firmly  to  the  boat,  in  which  case  the  velocity  of  the  boat  would 
be  augmented.     By  attentively  considering  this  and  all  analogous  ca- 
ses, we  shall  perceive  that  whenever  two  bodies  act  against  each 
other,  they  give  and  receive  equal  momenta,  and  the  momenta  being 
in  opposite  directions,  it  follows,  that  bodies  do  not  alter  the  quantity 
of  motion  they  have,  estimated  in  a  given  direction,  by  their  mutual 
action  on  each  other. 

47.  These  familiar  illustrations  may  serve  to  give  a  general  notion  of 
the  doctrine  of  action  and  reaction,  as  contained  in  the  third  law  of  mo- 


24 


MECHANICS, 


Fig.  5. 


tion  ;  but  this  law  is  susceptible  of  more  precise  experimental  proof  by 
means  of  the  following  apparatus,  (Fig.  5.)  Two  equal  bodies,  whose 
quantities  of  matter,  or  weights  are 
respectively  represented  by  A  and 
B,  are  suspended  contiguous  to 
each  other  by  strings  of  equal 
length.  A  is  pulled  from  its  per- 
pendicular position,  and  let  fall 
upon  B  at  rest.  This  space 
through  which  each  body  passes 
in  a  given  time,  as  indicated  by 
the  graduated  arc  5  Y,  is  a  mea- 
sure  of  its  velocity,  and,  in  all  ca- 
ses velocity  multiplied  into  the 
weight,  is  a  measure  of  the  momentum.  (Art.  22.)  From  experi- 
ments with  this  apparatus,  the  following  truths  are  established  :  (1.) 
That,  when  A  is  equal  to  B,  the  two  bodies  move  together  after  im- 
pact with  half  the  velocity  of  A  before  impact ;  and  since  the  quan- 
tity of  matter  in  both  is  double  that  of  A,  the  two  bodies  moving  with 
half  the  velocity  of  one  of  them,  have  the  same  momentum,  that  is,  the 
same  after  impact  as  before,  and  consequently  as  much  motion  as  A 
imparted  to  B  by  its  action,  just  so  much  B  took  from  A  by  its  reac- 
tion. (2.)  That,  when  A  is  greater  than  B,  it  still  holds  true  that  the 
momentum  of  the  mass  composed  of  both  bodies  united,  is  the  same 
after  impact  as  before :  consequently  B  extinguishes  in  A  just  as 
much  motion  as  it  receives  from  it.  (3.)  That  when  the  two  bodies 
move  in  opposite  directions,  the  quantity  of  motion  after  impact  is 
equal  to  the  difference  of  their  momenta  before  impact.  Thus  if 
A  and  B  are  equal,  and  they  meet  with  equal  velocities,  each  receiv- 
ing what  it  gives  in  an  opposite  direction,  both  are  brought  to  a  state 
of  rest.  If  B  has  half  the  velocity  of  A  then  it  will  extinguish  an 
equal  amount  in  A,  and  will  return  in  company  with  A  with  the  same 
velocity  as  before. 

48.  In  order  to  understand  the  doctrine  of  the  collision  of  bodies, 
it  is  necessary  to  advert  to  the  distinction  between  elastic  and  non- 
elastic  bodies.  Elastic  bodies  are  such  as  when  compressed,  restore 
themselves  to  their  former  state.  If  they  restore  themselves  with  a 


LAWS    OF    MOTION.  25 

force  which  is  equal  to  the  compressing  force,  then  they  are  said  to 
be  perfectly  elastic.  Sponge  is  a  substance  of  the  kind  which  pos- 
sesses greater  or  less  degrees  of  elasticity.  Glass,  ivory,  marble, 
and  steel,  are  among  the  most  elastic  substances  of  any  with  which 
we  are  acquainted.  Two  masses  of  lead,  or  earth,  when  struck  to- 
gether, scarcely  rebound  at  all,  and  are  therefore  non-elastic.  AJr, 
when  compressed,  restores  itself  with  a  force  equal  to  that  which 
compresses  it,  and  is  therefore  perfectly  elastic ;  but  most  of  the 
other  elastic  substances  above  mentioned,  possess  this  property  in  an 
imperfect  degree  only. 

1  In  the  experiments  mentioned  in  article  47,  the  impinging  bodies 
are  supposed  to  be  non-elastic. 

49.  In  the  collision  of  perfectly  elastic  bodies,  the  velocity  lost  by 
the  one  and  gained  by  the  other,  is  i?wicE  that  which  it  would  have 
been,  had  they  been  perfectly  non-elastic. 

Let  us  take  the  case  of  two  equal  bodies,  as  two  ivory  balls,  sup- 
posing each  to  be  perfectly  elastic,  and  calling  one  A  and  the  other 
B.  First,  let  A  overtake  B  moving  in  the  same  direction ;  then  B 
will  move  off  with  the  original  velocity  of  A,  and  A  will  move  with 
that  of  B ;  that  is,  the  two  will  interchange  their  velocities.  Sec- 
ondly, let  the  two  bodies  meet  from  opposite  directions  ;  each  will 
return  with  the  original  velocity  of  the  other.  Thirdly,  let  A  strike 
upon  B  at  rest ;  then  A  will  stop,  and  B  will  proceed  with  the  mo- 
tion A  had  before.  Again,  let^us  take  the  case  of  a  row  of  equal 
elastic  bodies  as 

A  BODE  X 

o  ooooo  o 

will  communicate  its  motion  to  B  and  stop  ;  and- thus  each  of 
the  bodies  will  successively  transmit  its  motion  to  the  next  body 
and  be  brought  to  rest,  while  the  last  body,  X,  will  move  off  with  the 
original  velocity  of  A. 

50.  It  is  a  general  law  in  the  material  world,  that  no  body  loses 
motion  in  any  direction,  without  communicating  an  equal  quantity  to 
other  bodies  in  that  same  direction ;  and  conversely,  that  no  body  ac- 

4 


26  MECHANICS. 

quires  motion  in  any  direction,  without  diminishing  the  motion  of 
other  bodies  by  an  equal  quantity  in  that  same  direction. 

This  law  of  motion  applies  not  only  to  the  impact  of  bodies, 
but  to  every  case  in  which  one  body  acts  upon  another.  It  holds 
good,  not  only  when  bodies  come  into  actual  contact,  but  when  they 
act  upon  one  another  at  any  distance  whatever.  A  body  A,  for  in- 
stance, is  sustained  by  another  body  B,  and  both  bodies  remain  at 
rest ;  if  the  pressure  exerted  by  the  two  bodies  were  not  equal,  it  is 
evident  that  some  motion  would  ensue  ;  which  is  contrary  to  the  sup- 
position. If  motion  does  ensue,  then  the  case  becomes  in  a  great 
measure,  analogous  to  that  of  impact;  and  the  effects  produced,  es- 
timated in  a  similar  manner,  are  found  to  observe  the  same  law.  The 
mutual  attractions  of  bodies  are  also  subject  to  this  law.  Thus  if 
two  equal  magnets, 'connected  with  two  equal  and  similar  pieces  of 
cork,  be  made  to  float  upon  the  surface  of  water ;  as  soon  as  they 
come  within  the  sphere  of  attraction,  they  are  observed  to  move  to- 
wards each  other  in  a  right  line,  with  equal  velocities,  and  conse- 
quently with  equal  momenta ;  and  as  the  resistance  which  each  body 
meets  with  from  the  fluid,  is  evidently  the  same,  we  infer  that  their 
actions  upon  each  other  are  equal. 

51.  Hence  it  follows,  that  the  sum  of  the  motions  of  all  the 
bodies  in  the  world,  estimated  in  one  and  the  same  line  of  direction, 
and  always  the  same  way,  is  eternally  and  invariably  the  same. 
Whatever  motion,  therefore,  one  body  receives  towards  another, 
whether  it  is  drawn  towards  it  by  attraction,  or  by  a  rope,  or  by  any 
other  method,  precisely  the  same  quantity  of  motion  it  imparts  to  the 
other  body  in  the  opposite  direction.     If  a  man  in  a  boat  pulls  at  a 
rope  attached  to   another  boat  of  equal  weight,   the  boats  will  move 
towards  each  other  with  equal  velocities  ;  but  a  man  in  a  boat  pull- 
ing a  rope  attached  to  a  large  ship  seems  only  to  move  the  boat,  but 
he  really  moves  the  ship  a  little,  although  its  velocity  is  as  much  less 
than  that  of  the  boat  as  its  weight  is  greater.     A  pound  of  lead  and 
the  earth-jittract  each  other  with  equal  force,  and  the  two  bodies  ap- 
proach each  other  with  equal  momenta.    (See  Art.  8.) 

52.  Since  momentum  is  proportioned  to  the  joint  product  of  the 
velocity  and  quantity  of  matter,  a  great  momentum  may  be  obtain- 


LAWS  OF  MOTION.  27 

ed,  either  by  giving  a  slow  motion  to  a  great  mass,  or  a  swift  motion 
to  a  small  body.  A  striking  illustration  of  this  is  afforded  by  ex- 
ample 4.  p.  11,  where  on  the  supposition  that  a  grain  of  light  moving 
with  its  usual  velocity,  were  to  impinge  directly  against. a  mass  of  ice 
floating  at  its  ordinary  slow  rate,  the  grain  of  light  would  be  compe- 
tent to  stop  about  sixty  five  tons  of  ice.  Islands  of  ice  move  with 
such  vast  momentum,  that  they  instantly  demolish  the  largest  ship 
of  war  if  it  comes  in  their  way. 

53.  If  a  body  in  motion  strikes  a  body  at  rest,  the  striking  body 
must  sustain  as  great  a  shock  from  the  cgllision  as  if  it  had  been  at 
rest,  and  struck  by  the  other  body  with  the  same  force.     For  the 
loss  of  force  which  it  sustains  in  one  direction,  is  an  effect  of  the 
same  kind  as  if,  being  at  rest,  it  had  received  as  much  force  in  the 
opposite  direction.     If  a  man  walking  rapidly,  or  running,  encount- 
ers another  standing  still,  he  suffers  as  much   from  the  collision  as 
the  man  against  whom  he  strikes.     When  two  bodies  moving  in  op- 
posite directions  meet,  each  body  sustains  as  great  a  shock  as  if,  be- 
ing at  rest,  it  had  been  struck  by  the  other  body  with  the  united  for- 
ces of  both.     For  this  reason,  two  persons  walking  in  opposite  di- 
rections, receive  from  their  encounter  a  more  violent  shock  than 
might  be  expected.     If  they  be  of  nearly  equal  weight,  and  one  be 
walking  at  the  rate  of  three  £nd  the  other  of  four  miles  an  hour,  each 
sustains  the  same  shock  as  if  he  had  been  at  rest,  and  struck  by  the 
other  running  at  the  rate  of  seven  miles,  an  hour.     This  principle 
accounts  for  the   destructive  effects  arising  from  ships  running  foul 
of  each  other  at  sea.     If  two  ships  of  500  tons  burden  encounter 
each  other,  sailing  at  ten  knots  an  hour,  each  sustains  the  shock 
which,  being  at  rest,  it  would  receive  from  a  vessel  of  1000  tons  bur- 
den sailing  ten  knots  an  hour.     It  is  a  mistake  to  suppose,  that  when 
a  large  and  a  small  body  encounter  each  other,  the  smaller  body  re- 
ceives a  greater  shock  than  the  larger.     The  shock  which  they  sus- 
tain is  the  same  ;  but  the  larger  body  is  better  able  to  bear  it.    When 
the  fist  of  a  pugilist  strikes  the  body  of  his  antagonist,  it  sustains  as 
great  a  shock  as  it  gives ;  but  the  part  being  more  fitted  to  receive 
the  blow,  the  injury  and  pain  are  inflicted  on  his  opponent.     This 
is  not  the  case,   however,  when  fist  meets  fist.     Then  the  parts  in 
collision  are  equally  sensitive  and  vulnerable,  and  the  effect  is  aggra- 


28  MECHANICS. 

vated  by  both  having  approached  each  other  with  great  force.  The 
effect  of  the  blow  is  the  same  as  though  one  fist,  being  held  at  rest, 
were  struck  with  the  combined  force  of  both. 

54.  The  question  may  be  asked,  why  are  the  effects  so  much 
more  injurious  to  fall  from  an  eminence  upon  a  naked  rock,  than  up- 
on a  bed  of  down  ?     In  both  instances  our  fall  is  arrested,  and  we 
sustain  a  contrary  and  equal  reaction ;  yet  in  the  one  case  we  might 
suffer  hardly  any  injury,  while  in  the  other,  we  should  be  bruised  to 
death.     The  reason  of  the  difference  is  this  :  when  we  fall  on  a  bed 
of  down,  the  resistance  is  Applied  gradually  ;  when  we  fall  on  a  rock 
it  is  applied  instantaneously.     We  do  not  strike  the  bed  with  the 
same  force  that  we  do  the  rock ;  we  move  along  with  the  bed,  and 
of  course  do  not  lose  our  motion  at  once,  and  we  receive  in  the  op- 
posite direction  merely  what  we  lose.     A  violent  blow,  if  equally 
diffused  over  the  human  body,  may  be  sustained   without  injury. 
Thus,  if  an  anvil  be  laid  on  the  breast,  a  man  may  receive  on  it  a 
heavy  blow  with  a  great  hammer  with  impunity. 

55.  There  are  many  instances  where  action  and  reaction  mutual- 
ly destroy  each  other,  and  no  motion  results.     Thus,  when  a  child 
stands  in  a  boat  and  pulls  by  a  rope  attached  to  the  stern,  he  labors 
in  vain  to  make  the  boat  advance.     Dr.  Arnott  tells  us  of  a  man 
who  attached  a  large  bellows  to  the  hinder  part  of  his  boat,  with  the 
view  of  manufacturing  a  breeze  for  himself,  being  ignorant  that  the 
reaction  would  carry  the  boat  backward,  as  much  as  the  impulse  of 
the  artificial  wind  carried  it  forward.     A  force  which  begins  and 
ends  with  a  machine  has  no  power  to  move  it. 

56.  The  three  Laws  of  motion,  which,  on  account  of  their  ex- 
tensive application  to  the  phenomena  of  motion,  we  have  endeavored 
to  render  familiar  to  the  learner  by  a  variety  of  illustrations,  are  to  be 
regarded  as  the  fundamental  principles  of  mechanics.     Their  truth 
rests  on  three  different  kinds  of  evidence  : 

1 .  They  are  conformable  to  all  experience  and  observation. 

2.  They  are  c6nfirmed  by  various  accurate  experiments. 

3.  The  conclusions  deduced  from  them  have  always  proved  true 
in  fact,  without  exception. 


VARIABLE  MOTION.  29 

CHAPTER  IV. 

OF  VARIABLE  MOTION. 

57.  When  a  moving  body  is  subjected  to  the  energy  of  a  force 
which  acts  on  it  without  interruption,  but  in  a  different  manner  at 
each  instant,  the  motion  is  called  in  general  variable  motion.     We 
have  instances  of  variable  motion  in  the  action  of  gun  powder  on  a 
ball  while  it  is  passing  through  the  barrel  of  a  gun,  and  in  the  action 
of  the  wind  on  the  sails  of  a  ship.     In  each  of  these  cases,  the  ve- 
locity of  the  moving  body  is  constantly  augmented,  yet  the  degree 
of  augmentation  is  diminishing  until  it  finally  ceases. 

When  a  moving  body  receives  each  successive  instant  the  same  in- 
crease of  velocity,  it  is  said  to  be  uniformly  accelerated.  If  a  small 
wheel  were  revolving  without  resistance,  and,  at  the  end  of  every 
second,  I  should  apply  a  given  impulse,  the  wheel  would  be  uniform- 
ly accelerated  ;  for,  by  its  own  inertia,  it  would  retain  all  its  previous 
motion,  and,  by  the  second  law  of  motion,  the  repetition  of  the  same 
force,  at  equal  intervals,  would  increase  its  velocity  at  a  uniform  rate. 
If  the  intervals  at  which  this  force  was  repeated  were  indefinitely 
diminished,  the  same  kind  of  effect  would  take  place;  and  the  same 
would  evidently  be  the  case,  were  the  force  to  operate  without  ces- 
sation. Such  a  force  is  that  of  gravity,  the  consideration  of  which 
will  be  pursued  in  the  following  sections. 
Falling  Bodies. 

58.  In  consequence  of  gravity,  all  bodies  near  the  earth  fall  to- 
wards its  center.     We  are  not  to  infer  from  this  fact,  that  there  is  any 
peculiar  force,  (like  that  of  a  large  magnet  for  example,)  residing  at 
the  center,  but  merely  that  the  effect  of  the  earth,  taken  as  a  whole, 
is  the  same  as  though  its  matter  were  condensed 

into  the  center.  Thus  in  Fig.  7,  if  we  con- 
sider how  a  body  at  A  would  be  attracted'  to- 
wards the  earth,  recollecting  that  every  parti- 
cle of  matter  in  the  earth  exerts  its  share  in  the 
effect,  we  shall  perceive  that  while  the  matter 
on  one  side  would  attract  it  to  the  right  of  the 
line  A  B,  the  matter  on  the  other  side  would 
attract  it  to  the  left  of  the  same  line  ;  conse- 
quently, both  together  would  carry  it  directly 


30  MECHANIC. 

forward  in  the  line  A  B  towards  the  center  ;  and  the  same  would  be 
true  were  the  body  A  placed  in  any  other  point  exterior  to  the  earth. 
The  leading  truths  respecting  falling  bodies  will  be  stated  in  the 
form  of  propositions,  which  the  learner  is  requested  to  commit  accu- 
rately to  memory.  The  illustrations  subjoined  to  each  will,  it  is  be- 
lieved, render  perfectly  intelligible  whatever  may  not  be  fully  under- 
stood from  the  proposition  as  enunciated. 

59.  I.   The  spaces  described  by  bodies  falling  from  a  state  of  rest 
under  the  influence  of  gravity,  are  proportioned  to  the  SQUARES  OF 
THE  TIMES,  during  which  they  are  falling. 

Thus,  if  a  body  be  let  fall  from  the  top  of  a  tower,  or  from  the 
brow  of  a  precipice,  it  will  fall  in  two  seconds  not  merely  twice  as 
far  as  in  one  second,  but  four  times  as  far ;  in  three  seconds  nine 
times  as  far ;  in  ten  seconds  one  hundred  times  as  far ;  and  so  on, 
the  spaces  being  proportioned,  not  simply  to  the  times  1,  2,  3,  and  10, 
but  to  their  squares,  1,  4,  9,  and  100. 

It  is  found  by  actual  experiment  that  the  space  through  which  a 
body  falls  in  one  second  from  a  state  of  rest,  is  16^  feet.  Hence, 
it  is  easy  to  estimate  the  space  corresponding  to  any  other  time ;  for 
the  space  belonging  to  two  seconds  must  be  4X16^,  or  64J  feet; 
to  three  seconds,  9  X 16-^,  or  144§  feet ;  and  to  ten  seconds,  100  X 
16^,  or  160SJ  feet.  To  find  the  number  of  feet  therefore,  through 
which  a  body  falls,  the  time  being  known,  we  have  the  following 
RULE.  Multiply  the  square  of  the  number  of  seconds  by  16^. 

Ex.  A  body  has  been  falling  7  seconds :  through  what  space  has 
it  fallen?  Ans.  788 rV  feet. 

60.  A  body  descending  by  gravity  is  in  the  same  situation  as  a  ball 
rolled  on  smooth  ice,  which  should  receive  a  new  impulse  every  mo- 
ment.    Retaining  all  its  previous  motion  and  receiving  more  contin- 
ually, its  speed  would  shortly  become  very  great ;  and  were  these 
new  accessions  of  velocity  without  intermission  and  uniform  (as  is 
actually  the  case  with  gravity)  the  velocity  acquired  would  be  propor- 
tioned^to  the  time  the  ball  had  been  moving ;  so  that  at  the  end  of 
two  seconds  it  would  be  twice  as  great  as  at  the  end  of  one  second ; 
at  the  end  of  ten  seconds  ten  times  as  great ;  and  so  on. 

61.  It  appears  from  the  foregoing  principle,  that  the  progress  of 
a  falling  body  is  rapidly  accelerated.     In  nature,  however,  the  resis- 


VARIABLE    MOTION.  31 

tance  of  the  air  prevents  a  body  which  falls  through  it,  from  acquir-  . 
ing  so  great  a  velocity  as  it  would  otherwise  do ;  still  we  see  indica- 
tions of  the  principle  of  acceleration,  in  the  impetuosity  with  which 
bodies  fall  from  any  considerable  height  above  the  earth.  Mete- 
oric stones  falling  from  the  sky,  sometimes  bury  themselves  deep 
in  the  ground.  Aeronauts  that  have  fallen  from  balloons  have  been 
dashed  in  pieces.  It  is,  however,  a  rare  occurrence  to  see  a  body 
falling  from  any  great  height  perpendicularly  ;  most  instances  of  ac- 
celerated motion  which  come  under  our  observation  are  bodies  falling 
down  inclined  planes,  where  the  same  law  of  acceleration  prevails. 
A  fragment  of  rock  descending  from  the  side  of  a  mountain,  has  its 
speed  augmented  as  it  goes,  until  its  momentum  becomes  irresistible, 
and  large  trees  are  prostrated  before  it. 

62.  II.  If  a  body  after  it  has  fallen  from  rest,  through  any  space, 
should  then  cease  to  receive  any  farther  impulse  from  gravity,  but 
should  proceed  on  uniformly  with  the  last  acquired  velocity,  it  would 
describe  TWICE  the  space  in  the  same  time  as  that  during  which  it  has 
fallen  to  acquire  that  velocity. 

Thus,  at  the  end  of  one  second  having  fallen  16T\  feet,  it  would 
have  acquired  a  velocity  which,  in  the  next  second,  would  carry  it 
32-J  feet;  at  the  end  of  four  seconds,  its  space  being  (4aXl6-f?) 
257J,  it  would,  without  any  farther  impulse  descend  during  the  next 
four  seconds  514|  feet. 

63.  III.  The  spaces  described  by  falling  bodies  are  also  proportioned 
to  the  squares  of  the  velocities  which  they  acquire  in  falling  over  those 
spaces. 

Ex.  1.  Through  what  space  must  a  body  fall  to  acquire  a  velocity 
of  60  feet  per  second  ?  In  falling  from  rest  16T^  feet  a  body  ac- 
quires a  velocity  of  32 £  feet ;  therefore,  the  square  of  the  velocity 
acquired,  that  is,  the  square  of  32|,  will  bear  the  same  ratio  to  its 
space,  namely  16^  feet,  that  the  square  of  60  bears  to  the  space 
required  ;  that  is,  (32i)2  :  16T'T : :  (60) 2  :  55-96  feet,  Ans.* 

*  Since  (32i)2=(2X16TV)2=22Xl6TVX16TV,  by  dividing  the  two 
first  terms  by  16^  we  have  Z2X[6^  :  1,  that  is,  641 : 1 ;  hence  to 
find  the  space  from  the  velocity,  we  derive  the  following  RULE.  Di- 
vide the  square  of  the  velocity  by  64£. 


32  MECHANICS. 

Ex.  2.  From  what  height  must  a  body  fall  to  acquire  a  velocity 
of  50  feet,  per  second?  Ans.  38.86  feet. 

64.  As  in  the  descent  of  a  body,  the  force  of  gravity  generates 
equal  increments  in  equal  times,  so  in  its  ascent,  equal  portions  of  ve- 
locity will  be  destroyed  in  equal  times;  that  is,  as  a  body  is  uniform- 
ly accelerated  as  it  falls,  so  it  is  uniformly  retarded  as  it  rises.  Hence, 

IV.  If  a  body  be  projected  perpendicularly  upwards,  with  the  ve- 
locity which  it  has  acquired  in  fatting  from  any  height,  it  ivill  rise 
to  the  height  from  which  it  fell,  before  it  begins  to  descend  again. 
It  will  also  occupy  the  same  time  in  rising  as  in  falling. 

Ex.  1.  To  what  height  will  a  body  rise,  when  projected  perpen- 
dicularly upwards  with  a  velocity  of  120  feet  per  second  ? 

As  it  will  rise  to  the  same  height  as  that  from  which  it  must  have 
fallen  to  acquire  this  velocity,  we  have  only  to  find  this  space.  Ac- 

(120)2 
cording  to  proposition  III, — gTT~  =  223.8  Ans. 

Ex.  2.  How  high  will  a  body  rise  when  thrown  perpendicularly 
upwards  with  a  velocity  of  100  feet, per  second?  Ans.  155.4  feet. 

65.  The  law  of  descent  of  falling  bodies,  as  enunciated  in  proposi- 
tion I.,   (Art.  59.)  goes  on  the  supposition  that  the  body  begins  its 
descent  from  a  state  of  rest,  and  that  it  afterwards  receives  no  im- 
pulse from  any  force  beside  gravity  ;  but  we  may  have  occasion  to 
estimate  the  motion  of  a  falling  body  which  receives,  either  at  first 
or  during  ks  descent,  an  impulse  from  some  extraneous  force.     In 
this  case  we  must  add  the  amount  of  the  impulse  to  the  ordinary 
force  of  gravity,  as  expressed  in  the  following  proposition. 

V.  The  space  described  in  any  given  time  by  a  body  projected 
downwards  with  a  given  velocity,  is  equal  to  the   space  which  would 
be  described  with  that  velocity  continued  uniformly  for  that  time,  to- 
gether with  the  SPACE  through  which  a  body  would  fall  from  rest  by 
the  action  of  gravity  for  the  same  time. 

Ex.  1.  A  body  is  projected  downwards  with  a  velocity  of  30  feet 
in  a  second :  how  far  will  it  fall  in  4  seconds  ? 


VARIABLE    MOTION.  33 

First,  by  a  uniform  motion  of  30  feet  for  four  seconds,  the  body 
would  describe       -  -     120    feet. 

Secondly,  by  gravity  it  would,  in  the  same  time  describe  257  J 


Hence,  the  entire  space  is  377J  feet. 

Ex.  2.  A  body  after  falling  3  seconds  passes  by  a  window  in  a 
tower,  from  which  a  person  standing  in  the  tower,  gives  it  a  blow 
downwards,  which  increases  its  velocity  20  feet  per  second,  after  which 
it  falls  during  2  seconds  more  and  then  reaches  the  ground  :  what  is 
the  height  from  which  it  fell  ? 

First,  the  descent  by  gravity  for  5  seconds,  is       -       402^  feet. 

Secondly,  the  uniform  motion  of  20  feet  for  2  seconds,  is,  40 

Whole  space  442TV 

Ex.  3.  Suppose  a  body  to  be  projected  downwards  with  a  velo- 
city of  17  feet  per  second  :  how  far  will  it  fall  in  5  seconds?  Ans. 
487T'a  feet. 

66.  The  laws  of  falling  bodies  are  susceptible  of  very  accurate 
experimental  proof  by  means  of  Atwood's  Machine  (Art.  32).  Be- 
fore the  invention  of  this  apparatus,  there  were  two  difficulties  in  the 
way  of  such  a  verification,  namely,  the  little  time  occupied  in  de- 
scending through  such  perpendicular  heights  as  the  experimenter 
can  command,  and  the  resistance  of  the  air,  whicji,  when  the  velo- 
city becomes  great,  acts  as  a  powerfully  retarding  force.  We  can 
rarely  command  a  perpendicular  eminence  of  more  than  400  feet, 
and  yet  the  time  of  passing  over  this  space  is  only  about  five  sec- 
onds, a  period  too  short  to  enable  us  to  mark  distinctly  the  respect- 
ive rates  at  which  the  successive  intervals  are  described.  Atwood's 
Machine  affords  the  means  of  obviating  both  these  difficulties,  and 
of  verifying  the  laws  of  falling  bodies  with  great  accuracy.  The  ob- 
ject of  the  machine,  so  far  as  it  respects  experiments  on  falling  bod- 
ies, is  to  render  the  descent  of  bodies  so  gradual,  that  the  relations 
between  the  times  and  spaces  can  be  accurately  observed.  By  re- 
currence to  the  figure,  and  to  the  description  given  in  art.  32,  we  shall 
readily  see  how  this  object  is  accomplished.  The  weights  D  and  E 
are  each  equal  to  31 J  oz.  and  of  course  the  quantity  of  matter  in  both 
is  63  ounces.  Now,  since  one  of  these  weights  rises  as  the  other  de- 
scends, the  force  of  gravity  retards  the  one  as  much  as  it  accelerates 

5 


34 


MECHANICS. 


the  other,  and  they  are  in  effect  the  same  as  though  they  were  en- 
tirely destitute  of  gravity.  If  a  small  weight,  as  one  ounce,  were 
let  fall  freely  from  the  top  of  the  machine,  it  would  fall  through  this 
small  space  almost  in  an  instant,  and  we  should  be  uanble  to  mark  the 
rate  at  which  it  passed  over  the  successive  portions  of  the  scale  FG; 
but  if  it  be  laid  on  the  weight  D,  it  must  carry  D  along  with  it ;  that 
is,  it  must  make  D  descend  and  E  ascend,  and  therefore  the  motion 
belonging  to  one  ounce,  will  be  distributed  through  64  ounces,  and 
the  velocity  retarded  in  the  same  ratio.  Consequently,  the  weight 
D  will  descend  only  ^th  part  as  fast  as  a  body  falling  freely ;  and 
as  a  body  falling  freely  descends  about  16  feet,  or  192  inches  in 
one  second,  the  weight  D  will  descend  y/  =  3  inches  in  the  same 
time.  The  comparative  progress  of  this  weight,  and  of  a  body  fall- 
ing freely  for  several  successive  seconds,  will  be  seen  in  the  follow- 
ing table. 


Time,  in  seconds, 

1 

2 
64£ 

3 

A 

| 
402T', 

6 

Body  falling  freely,  in  feet, 

16T', 

144J 

257J 

579 

Do.  in  Atwood's  Machine,  in  inch's, 

2 

12 

27 

48 

75 

108 

67.  Hence  it  appears,  that  in  6  seconds,  while  a  body  would  fall 
freely  through  579  feet,  it  would  in  the  same  time  descend  only  9 
feet  in  Atwood's  Machine.     But  the  latter  is  a  uniformly  accelera- 
ted velocity,  and  subject  to  the  same  laws  as  the  former  and  it  may 
therefore  be  employed  to  investigate  the  laws  of  falling  bodies.     The 
results  correspond  remarkably  with  theory,  so  that  when  the  instru- 
ment is"  well  constructed   and  managed   skilfully,  the  descending 
weight  clicks  upon  the  stage  or  brass  plate  K,  at  the  very  instant 
required. 

68.  It  is  not  alone  by  the  direct 
fall  of  bodies  that  the  gravitation  of 
the   earth  is  manifested.     The  cur- 
vilinear motion  of  bodies  projected  in 
directions  different  from  the  perpen- 
dicular, is  a  combination  of  the  effects 
of  the  unijbrm  velocity  which  has  been 
given  to  the  body  by  the  impulse  which 
it  has  received,  and  the  accelerated  or 
retarded   velocity   which  it  receives 
from  the  earth's  attraction.  Suppose  a 
body  placed  at  any  point  P  (Fig.  8.) 


VARIABLE    MOTION.  35 

above  the  surface  of  the  earth,  and  let  P  A  be  the  direction  of  the 
earth's  center.  If  the  body  were  allowed  to  move  without  receiving 
any  impulse,  it  would  descend  to  the  earth  in  the  direction  P  A, 
with  an  accelerated  motion.  But  suppose  that  at  the  moment  of  its 
departure  from  P,  it  receives  an  impulse  in  the  direction  PB ;  then 
it  would  fall  towards  the  earth,  between  the  actions  of  the  two  forces, 
in  the  curve  line  P  D.  The  greater  ihe  velocity  of  projection  in  the 
direction  P  B,  the  greater  sweep  the  curve  will  take.  Thus  it  will  suc- 
cessively take  the  forms  P  D,  P  E,  P  F,  &c.  until,  when  the  velocity 
of  projection  is  increased  to  a  certain  amount,  the  body  would  sweep 
quite  clear  of  the  earth,  and  revolve  around  it,  as  the  moon  does  around 
the  earth.  Thus  a  cannon  ball  shot  horizontally  from  the  top  of  a  lofty 
mountain,  would  go  three  or  four  miles.  If  there  were  no  atmos- 
phere to  resist  its  motion,  the  same  original  velocity  would  carcy  it 
thirty  or  forty  miles  before  it  fell ;  and  if  it  could  be  dispatched 
with  about  ten  times  the  velocity  of  a  cannon  shot,  the  centrifugal 
force  would  exactly  balance  the  force  of  gravity,  and  the  ball  would 
go  quite  round  the  earth. 

69.  Hence  it  is  obvious,  that  the  phenomenon  of  the  revolution 
of  the  moon  round  the  earth,  is  nothing  more  than  the  combined  ef- 
fects of  the  earth's  attraction,  and  the  impulse  which  it  received  when 
launched  into  space  by  the  hand  of  its  Creator ;  and  were  any  of 
the  heavenly  bodies  to  explode,  we  may  conceive  that  the  frag- 
ments would  proceed  in   a  rectilinear  direction,  until  approaching, 
severally,  within  the  sphere  of  influence  of  some  large  body,  whose 
attraction  would  combine  with  their  projectile  force,- they  would 
forever  afterwards  continue  to  revolve  around  that  body,  as  the  sat- 
ellites revolve  around  the  primary  planets. 

70.  The  attraction  of  gravitation  is  manifested  by  comparatively 
small  masses  of  matter.     The  effect  of  a  high  mountain  is  percep- 
tible upon  a  plumb  line,  causing  it  to  deviate  sensibly  from  a  perpen- 
dicular, so  that  the  same  star  in  the  zenith  would  change  its  appa- 
rent place  when  viewed  on  opposite  sides  of  the  mountain. 


36  MECHANICS: 

CHAPTER  V. 

OF  COMPOSITION  AND  RESOLUTION  OF  MOTION. 

71.  SIMPLE   motion  is  that  which  arises  from  the  action  of  a 
single  force ;  compound  motion  is  that  which  is  produced  by  several 
forces  acting  in  different  directions.     Strictly  speaking,  we  have  no 
example  of  a  simple  motion,  since  in  the  absolute  motion  of  all  bo- 
dies, their  own  proper  motion  is  combined  with  that  of  the  earth  in 
its  diurnal  and  annual  revolutions,  and  we  know  not  with  how  many 
others.     In  an  enlarged  sense  therefore  all  motions  are  compound. 
But  in  the  foregoing  distinctions  we  have  reference  only  to  relative  mo- 
tions, as  those  which  take  place  among  bodies  on  the  earth. 

72.  When  a  body  is  acted  upon  at  the  same  time,  by  two  or  more 
forces,  whose  directions  are  not  in  the  same  straight  line,  it  is  evi- 
dent that  it  will  deviate  from  the  course  in  which  it  would  have  mo- 
ved by  the  single  action  of  either  of  those  forces,  and  will  proceed 
in  some  intermediate  direction.     Let  .us  first  consider  the  case  of  a 
body  acted  upon  by  two  forces. 

If  I  place  a  small  ball  at  one  of  the  corners  of  a  table,  and  give 
it  a  snap  with  my  thumb  and  finger,  in  a  direction  parallel  to  one 
edge  of  the  table,  it  will  of  course  move  along  that  edge ;  or  if  I 
give  the  impulse  with  the  thumb  and  finger  of  the  other  hand,  in  the 
direction  of  the  edge  which  is  at  right  angles  to  the  former,  the  ball 
will  move  along  this  edge ;  but  if  I  give  both  these  impulses  at 
the  same  moment,  the  ball  will  move  diagonally  across  the  table 
from  corner  to  corner.  If  the  force  applied  to  each  be  accurately 
proportioned  to  the  length  of  the  corresponding  side  of  the  table, 
(as  it  may  be  by  means  of  springs  fixed  to  the  corner  of  the  table,) 
the  ball  will  reach  the  opposite  corner  in  the  same  time,  as  it  would 
have  taken  it  to  describe  either  side  separately.  This  fact  is  gene- 
ralized jn  the  following  fundamental  proposition. 

73.  Tivo  impulses,  which,  when  communicated  separately  to  a  bo- 
dy would  make  it  describe  the  adjacent  sides  of  a  parallelogram  in 
ft  given  time,  will,  when  they  are  communicated  at  the  same  instant, 


COMPOSITION    AND    RESOLUTION    Olf    MOTION. 

cause  it  to  describe  the  diagonal  in  the  same  time  ;  and  the  motion  in 
the  diagonal  will  be  uniform. 

Suppose  a  body  pla-  Fig-  9- 

cedatA  (Fig.  9.)  to  be 
acted  upon  by  two  for- 
ces, one  of  which  would 
cause  it  to  move  uni- 
formly over  the  line 
AB,  and  the  other  over 
the  line  AC  in  the  same  A 
time,  then  if  both  forces  act  at  the  same  instant  upon  the  body,  it 
will  by  their  joint  action  move  uniformly  over  the  diagonal  AjfJ  in 
the  same  time  it  would  have  taken  to  describe  AB  or  AC  by  the 
forces  acting  separately.  By  the  second  law  of  motion,  every  force 
applied  to  a  body  produces  the  same  change  of  motion  as  though  it 
were  the  only  force  applied.  Consequently  the  force  applied  in  the 
direction  of  AC  will  carry  a  body  just  as  far  towards  the  line  CD  as 
though  the  force  which  acts  in  the  direction  of  AB  were  not  applied. 
In  the  same  manner,  by  the  other  force  it  will  be  carried  just  as  far 
towards  BD  as  though  there  were  no  other  force  acting  upon  it. 
Hence,  the  body  will  be  found  both  in  the  lines  CD  and  DB,  when 
acted  upon  by  the  two  forces  conjointly,  in  the  same  time,  that  it 
would  reach  those  lines  respectively  if  acted  on  by  each  force  sepa- 
rately. Being  therefore  at  the  end  of  this  time  in  both  the  lines,  it 
must  be  at  their  intersection,  that  is,  at  the  point  D. 

74.  Since  AB  is  equal  to  CD  and  parallel  to  it,  the  two  forces  may 
be  considered  as  acting  in  the  direction  of  the  two  sides  AC  and  CD  of 
the  triangle  ACD ;  and  hence  when  a  body  would  describe  the  two 
sides  of  a  triangle  by  two  forces  acting  separately,  it  will  in  the  same 
time,  describe  the  third  side  by  the  two  forces  acting  jointly. 

75.  We  daily  observe  examples  strikingly  illustrative  of  the  principle 
just  explained.     In  crossing   a  river,  the  boatman  heads  up  the 
stream,  and  so  combines  the  direction  of  the  boat  with  that  of  the 
currents,  as  to  move  directly  across  in  a  line  which  is  the  diagonal  be- 
tween the  two  directions  j  or  he  describes  the  third  side  of  a  triangle 
by  the  action  of  two  forces  which  would  severally  carry  him  over  tlin 


38 


MECHANICS. 


other  two  sides.  Rowing,  swimming,  and  flying  are  severally  in- 
'  stances  of  motion  in  the  diagonal  between  two  forces.  In  feats  of 
horsemanship,  when  the  rider  leaps  up  from  his  saddle,  we  are  sur- 
prised not  to  see  the  horse  pass  from  under  him  ;  but  he  retains  the 
the  motion  he  has  in  common  with  the  horse,  and  does  not  in  fact  as- 
cend perpendicularly,  but  obliquely,  rising  in  one  diagonal  and  fall- 
ing in  another.  Two  men  in  a  boat  under  rapid  sail,  sitting  on  op- 
posite sides  and  tossing  the  ball  from  one  to  the  other,  catch  the  ball  in 
the  same  manner  as  though  they  were  at  rest.  While,  indeed,  the 
ball  is  crossing  the  boat,  the  opposite  man  advances;  but  the  ball  also 
participating  in  the  same  common  motion  of  the  boat,  advances  mean- 
while in  the  same  manner,  and  in  reaching  the  other  side,  actually 
moves  diagonally,  with  respect  to  the  surrounding  space,  though  with 
respect  to  the  boat  its  motion  is  directly  across.  A  body  let  fall  from 
the  top  of  a  mast,  when  the  ship  is  under  sail,  falls  along  down  the 
mast  and  strikes  at  its  foot  in  the  same  manner  as  though  the  ship  were 
at  rest,  partaking  of  the  common  motion  of  the  ship,  and  therefore 
describing  a  diagonal  between  this  forward  direction  and  that  of  gravity. 

76.  If  a  body  be  impelled  by  any  number  offerees  which,  acting 
separately,  would,  in  a  given  time,  make  it  describe  all  the  sides  of 
a  polygon,  except  the  last  side;  ivhen  all  these  forces  act  at  the  same 
instant,  the  body  will  be  made  to  describe  the  remaining  side  in  the 
same  time. 


Fig.  10. 


Thus  in  Fig.  10,  a  body  pla- 
ced at  A,  and  acted  on  by  two 
forces  represented  in  quantity  and 
direction  by  AB  and  BC,  would 
describe  the  side  AC.  Therefore, 
AC  may  be  taken  as  the  equiva- 
lent of  those  two  forces,  Or  as  the 
representative  of  a  force  equal  to 
them  both,  and  producing  pre- 
cisely ther  same  effects  as  they 
would  do.  For  the  same  reason 
the  two  forces  AC  and  CD  would  cause  the  body  to  to  describe  AD  ; 
and  AD,  therefore,  represents  a  force  equivalent  to  the  three  forces 
AB,  AC,  CD,  and  may  be  substituted  for  them  ;  and,  in  like  man- 


COMPOSITION    AND    RESOLUTION    OF    MOTION. 


39 


ner  AE  may  be  substituted  for  AD  and  DE.  Therefore  under  the 
action  of  the  several  forces  AB,  BC,  CD,  and  DE,  the  body  would 
describe  the  last  side  AE. 

77.  If  the  number  of  forces  were  equal,  in  quantity  and  direction, 
to  all  the  sides  of  the  polygon,  then  the  body  would  remain  at  rest 
under  their  joint  action.     For  the  forces  acting  in  the  direction  of 
AE,  would  in  this  case  be  exactly  balanced  by  those  acting  in  the 
direction  of  EA. 

78.  A  given  motion  may  be  D  FiS-  11< 
considered  as  caused  by  two, 

three,  or  any  number  of  forces 

as  will  be  evident  from  the  fol- 

lowing figure.     AB  will  repre- 

sent a  motion  resulting  either 

from  the  combined   action  of 

forces  represented  in   quantity 

and  direction,  by  AD  and  DB, 

or  from  AC  and  CB,  or  from 

the   sides  of  various  other  tri- 

angles  of  which  AB  may  be 

considered  as  the  third  side.     In  the  same  manner,   any  one  side  of 

the  polygon,  (Fig.  10.)  may  be  considered  as  the  representative  of 

a  motion  produced  by  forces  corresponding  to  all  the  other  sides  of 

the  figure. 

79.  JL  given  force  may  be  resolved  into  an  unlimited  number  of 
others,  .acting  in  all  possible  directions. 

Thus  (Fig.  11.)  AD  and  DB,  or  AC  and  CBmay  be  substituted 
for  AB,  representing  forces  which  are  equivalent  to  that  represented 
by  AB  ;  and  any  force  represented  by  one  side  of  the  polygon 
(Fig.  10.)  may  be  resolved  into  forces  corresponding  to  all  the  other 
sides,  the  united  effect  of  which  is  only  equal  to  that  of  this  side. 

The  sailing  of  a  ship  affords  an  instructive  illustration  of  the  princi- 
ples of  the  composition  and  resolution  of  motion.  To  one  unacquaint- 
ed with  these  principles,  it  is  apt  to  appear  mysterious  that  a  ship  is 
able  to  sail  with  a  wind  partly  ahead,  and  still  more  that  two  ships 
are  able  to  sail  in  exactly  opposite  directions  by  the  same  wind.  Let 
us  see  how  this  takes  place. 


40 


MECHANICS* 


Fig.  12. 


Let  AB  (Fig.  12.)  repre- 
sent the  keel  of  a  ship,  and 
CD  the  sail ;  and  let  the  wind 
come  in  from  the  side,  in  the 
direction  of  HD.  Let  DE 
represent  the  whole  force  of 
the  wind,  and  resolve  it  into 
two  forces,  viz.  into  EF  per- 
pendicular, and  FD  parallel 
to  the  sail  DC.  Then  it  is 
manifest  that  EF  alone  re- 
presents the  effective  force  of 
the  wind  upon  the  sail.  But 
EF  is  not  wholly  employed  inxurging  the  ship  forward,  since  it  is  ob- 
lique to  her  course ;  therefore,  again  resolve  EF  into  FG  parallel 
with  the  course  and  GE  at  right  angles  with  it.  The  force  re- 
presented by  GE  is  lost  by  the  lateral  resistance  of  the  water,  or  is 
counteracted  by  the  helm,  while  FG  is  employed  in  propelling  the 
ship  on  her  way. 

By  inspecting  Fig.  12.  it  will  readily  be  seen  that  another  ship 
may  sail  in  the  opposite  direction  by  the  same  wind ;  only  the  sail  is 
raised  on  the  left  side  when  the  ship  is  heading  one  way,  and  on  the 
right  side  when  it  is  heading  the  other  way.  When  the  wind  strikes 
the  sail  at  right  angles,  only  one  resolution  is  necessary ;  for  if  FE 
represents  the  whole  force  of  the  wind,  FG  will  represent  the  force 
which  propels  the  ship  forward,  while  GE  will  represent  the  part 
which  is  lost  by  the  lateral  resistance  of  the  water. 

80.  Since,  resolving  the  force  of  the  wind  after  the  foregoing 
manner,  the  effective  part  of  the  force,  viz.  FG,  will  not  wholly  dis- 
appear until  the  wind  is  directly  ahead,  it  might  seem  possible  to  sail 
much  nearer  the  wind  than  is  found  to  be  actually  practicable.     But 
though  on  account  of  the  peculiar  shape  of  vessels,  the  forward  re- 
sistance is  much  less  than  the  lateral,  yet  it  is  something,  and  there- 
fore retires  more  or  less  of  the  force  that  acts  parallel  to  the  keel  to 
overcome  it. 

81.  «/2  body  acted  upon  at  the  same  time  by  three  forces  represented 
in  quantity  and  direction  by  the  three  sides  of  a  triangle  taken  in  or- 
der, (or  by  lines  parallel  to  these)  will  remain  at  rest. 


COMPOSITION    AND    RESOLUTION    OF    MOTION.  41 

Since  AD  (Fig.  9.)  represents  a  force  which  is  equivalent  to  those 
corresponding  to  the  two  sides  AC,  CD,  if  upon  a  body  placed  at  A, 
two  such  forces  were  to  act  while  a  third  force  corresponding  to  the 
side  DA  were  to  act  upon  it  in  the  direction  DA,  the  body  being  acted 
upon  by  two  opposite  and  equal  forces  would  remain  at  rest.* 

82.  A  kite  at  rest  in  the  air  is  commonly  mentioned  as  an  exam- 
ple of  this,  the  three  forces  being,  the  direction  of  the  wind,  the 
weight  of  the  kite,  and  the  action  of  the  string.  Let  AB  be  a  kite, 
held  by  the  string  AS.  Let  DF  represent  the  force  of  the  wind 
blowing  horizontally,  and  resolve  it  into  two  forces,  viz.  DC  perpen- 


dicular and  CF  parallel  to  the  kite.  Then  DC  will  be  the  only  ef- 
fective part  of  the  wind,  since  that  part  which  acts  parallel  to  the 
kite,  can  have  no  influence  on  its  motions.  Again,  resolve  CD  into 
two  forces,  namely,  CE  perpendicular  and  DE  parallel  to  the  hori- 
zon. Then  CE  will  represent  the  upward  force  of  the  wind,  and 
DE  its  force  in  a  horizontal  direction.  Now  when  the  string  AS 
makes  such  an  angle  with  the  kite  that  its  downward  force  AG, 
added  to  the  weight  of  the  kite,  shall  equal  CE,  and  its  horizontal 
force  HG  shall  equal  DE,  the  kite  will  be  at  rest. 

83.  When  two  motions  which  are  not  in  the  same  straight  line  are 
combined,  one  of  which  is  uniform  and  the  other  accelerated,  the 
moving  body  describes  a  curve. 

*  The  three  forces  are  properly  represented  by  AC  and  AB  acting 
against  DA;  but  CD  is  parallel  amjl  equal  to  AB,  and  may  therefore 
be  substituted  for  it. 


MECHANICS. 


Fig.  14. 


Thus,    (Fig.   14.)    when   a   body   is  N 
thrown  obliquely  upwards  in  the  direc- 
tion of  PN,   the  force  of  gravity  will 
draw  it  continually  away  from  that  line* 
towards  the  earth ;  and  as  gravity  is  a 
force  which  increases  the  motion  of  a 
falling  body  every  instant,  the  body  will   Q 
at  first  recede  slowly  from  the  line  PN, 
but  more  and  more  rapidly  as  it  advan- 
ces, describing  a  curve  whose  deviation 
from  the  line  of  projection  continually 

increases,   as  POQ.     Now,  the  spaces  X4V 

PM  and  PN,  representing  the  uniform  motion  in  the  line  of  projec- 
tion are  to  one  another  as  the  squares  of  the  spaces  MO  and  NQ 
which  represent  the  descent  towards  the  earth.  But  a  curve  de- 
scribed between  two  forces  bearing  this  relation  to  each  other,  is 
known  to  be  .the  curve  called  a  parabola,  being  one  of  the  curves 
which  result  from  the  sections  of  a  cone.  The  parabola,  therefore, 
is  the  curve  ^belonging  to  all  bodies  projected  from  the  earth  into  the 
atmosphere,  as  is  seen  when  a  stone  is  thrown  upwards,  or  a  fluid 
spouts  obliquely.  Forces  differently  proportioned  to  each  other, 
describe  different  curves,  as  circles,  ellipses,  &c.  Thus,  the  planets 
revolve  around  the  sun  in  ellipses,  between  the  force  of  projection 
and  that  of  attraction  towards  the  central  luminary. 


CHAPTER  VL 

OF  THE  CENTER  OF  GRAVITY. 

84.  The  center  of  gravity  of  a  body  is  that  point,  about  ivhich, 
if  supported,  all  the  parts  of  a  body  (acted  upon  only  by  the  force  of 
gravity)  would  balance  each  other  in  any  position.  Thus,  a  staff 
poised  across  the  finger,  rests  only  when  the  finger  is  under  the  cen- 
ter of  gravity. 

The  principles  which  have  been  discovered  respecting  the  com- 
position and  resolution  of  forces,  and  respecting  the  center  of 
gravity,  have  alike  contributed  greatly  to  simplify  the  doctrines  -of 
Mechanics.  It  is  characteristic  of  a  great  and  penetrating  mind,  to- 


CENTER    OF    GRAVITY. 


43 


devise  means  of  divesting  intricate  subjects  of  their  complexity  and 
thus  to  bring  easily  within  the  grasp  of  the  mind,  subjects  otherwise 
too  much  involved  to  be  within  its  comprehension.  By  the  rule  of 
simple  multiplication,  we  easily  multiply  any  number  by  one  thousand : 
indeed,  it  is  nothing  more  than  to  annex  three  cyphers  to  the  number 
itself;  but  how  tedious  would  be  this  process,  were  the  rule  of  multipli- 
cation undiscovered,  and  we  were  unacquainted  with  any  other  method 
of  arriving  at  the  result,  except  to  add  the  given  number  to  itself  one 
thousand  times.  In  like  manner  by  means  of  the  rules  for  the  com- 
position of  motion,  we  are  enabled  to  reduce  a  thousand  different 
motions  to  one ;  and  by  the  doctrine  of  the  center  of  gravity  we  are 
taught  how  we  may  make  a  force,  situated  at  one  single  point,  equiv- 
alent to  an  infinite  number  of  forces,  situated  in  as  many  different 
points ;  and,  instead  of  pursuing  the  endless  diversities  of  motion 
to  which  the  different  parts  of  a  complicated  system  of  bodies  may 
be  subject,  we  are  taught  how  to  follow  merely  the  motions  of  a  sin- 
gle individual  point. 

85.  In  regular  plane  figures,  such  as  squares,  parallelograms,  cir- 
cles, fyc.  the  center  of  gravity  is  the  same  with  the  center  of  the  figure. 
In  the  following  figures,  the  lines  AB  and  CD,  (Fig.  15.)  bisect  each 

Fig.  15. 


B  AM 


D 


D 


other  in  the  center  $f  the  figure.  Each  line  obviously  has  its  center 
of  gravity  in  the  point  of  bisection,  and  that  is  the  point  where  the 
quantities  of  matter  on  all  sides  are  equal,  and  therefore  exactly  bal- 
ance one  another.  The  same  is  true  of  such  regular  solid  figures  as 
a  cube,  a  sphere,  a  cylinder,  &c. 

86.  To  find  the  center  of  gravity  by  experiment,  several  different 
methods  present  themselves.  We  will  first  suppose  the  body  to  be 
in  the  shape  of  a  piece  of  board,  of  uniform  thickness.  Suspend  it 
by  one  corner,  and  from  the  same  corner  let  fall  a  plumb  line,  and 


44  MECHANICS. 

mark  its  line  of  direction  on  the  surface  of  the  board.  Suspend  the 
board  from  any  other  point,  and  mark  the  line  of  direction  of  the 
plumb  line  as  before,  and  the  point  where  these  lines  intersect  each 
other,  must  obviously  be  the  center  of  gravity,  since  that  center  is 
in  both  of  the  lines. 

87.  But  when  the  body  is  not  of  uniform  thickness,  but  is  any 
irregular  solid,  suspend  the  body  by  a  thread,  and  let  a  small  hole  be 
bored  through  it,  in  the  exact  direction  of  the  thread,  so  that  if  the 
thread  were  continued  below  the  point  where  it  is  attached  to  the 
body,  it  would  pass  through  this  hole.     The  body  being  successively 
suspended  by  several  different  points  in  its  surface,  let  as  many 
small  holes  be  bored  through  it  in  the  same  manner.     If  the  body 
be  then  cut  through,  so  as  to  discover  the  directions  which  the  sev- 
eral holes  have  taken,  they  will  be  all  found  to  cross  each  other  at 
one  point  within  the  body.     Or  the  same  fact  may  be  discovered 
thus :  a  wire  which  nearly  fills  the  holes  being  passed  through  any 
one  of  them,  it  will  be  found  to  intercept  the  passage  of  a  similar 
wire  through  any  other. 

88.  A  convenient  method  of  finding  the  center  of  gravity  of  a 
body  is,  to  balance  it  in  different  positions  across  a  thin  edge,  as  the 
edge  of  a  knife  or  a  prism.     The  same  thing  may  be  effected,  when 
the  shape  of  the  body  will  admit  of  it,  by  laying  it  on  the  edge  of  a 
table,  and  letting  so  much  of  it  project  over  the  edge,  that  the  slight- 
est disturbance  will  cause  it  to  fall.     The  center  of  gravity  is  the 
point  in  which  the  several  lines  marked  on  the  body,  where  the  edge 
cuts  it,  intersect  one  another.     From   some  or  all  of  the  foregoing 
trials,   the  center  of  gravity  of  bodies  may  be  ^nearly  ascertained  ; 
but  in  order  to  find  it  with  absolute  exactness,  we  are  frequently 
obliged  to  resort  to  intricate  mathematical  processes. 

By  whatever  method  the  center  of  gravity  of  a  body  has  been 
ascertained,  we  shall  find  that  when  that  is  supported,  the  body 
will  remain  at  rest  in  every  position.  Thus  a  globe  will  stand  se- 
curely on  a*very  small  perpendicular  support,  since  that  support  will 
necessarily  be  under  the  center  of  gravity;  a  lever,  as  the  beam  of 
a  balance,  poised  on  its  center  of  gravity,  will  be  at  rest  in  every  po- 
sition it  takes  while  turning  round  the  fulcrum,  and  however  irregu- 


CENTER    OF    GRAVITY.  45 

lar  the  body  may  be,  it  will,  when  balanced  on  its  center  of  gravity, 
obstinately  maintain  its  position. 

89.  We  may  find  the  distance  of  the  common  center  of  gravity 
of  any  number  of  bodies  from  a  given  point,  upon  the  following 
principles. 

First,  suppose  the  bodies  have  their  centers  of  gravity  in  the  same 
right  line,  as  in  figure  16,  then  the  distance  of  the  common  center  of 

Fig.  16. 
A  B  C  D 


O  G 

gravity  of  all  the  bodies  from  the  point  O,  will  be  found  by  multiply- 
ing each  body  into  its  distance  from  that  point,  and  dividing  by  the 
sum  of  the  bodies.  Indeed,  it  is  not  essential  that  the  matter  in 
question  should  even  reside  in  one  and  the  same  mass,  for  this  prin- 
ciple holds  good  for  any  number  of  separate  bodies. 

90.  In  figure  16,  A,  B,  C,  D,  are  bodies  of  different  weights  con- 
nected together  by  a  wire  which  is  balanced  on  the  center  of  gravity 
G.     Now  we  may  find  the  distance  of  G  from  any  point  O  in  the 
same  line,  by  multiplying  A  into  AO,  B  into  BO,  C  into  CO,  and 
D  into  DO,   and  dividing  the  sum  of  these  products  by  the  sum  of 
the  bodies  A,  B,  C  and  D.     Secondly,  suppose  that  the  bodies  are 
not  in  the  same  right  line,  but  are  situated  like  a^number  of  balls  of 
different  weights  hanging  at  different  distances  from  the  ceiling  of  a 
room.     Thus,  we  may  find  the  distance  of  their  common  center  of 
gravity  from  the  perpendicular  wall  of  the  room,  by  multiplying  each 
body  into  its  distance  from  the  wall,  and  dividing  the  sum  of  the  pro- 
ducts by  the  sum  of  the  bodies. 

91.  When  a  body  is  supported  by  a  prop  placed  under  its  center 
of  gravity,  the  pressure  will  be  the  same,  whether  this  whole  quantity 
of  matter  be  uniformly  diffused  through  the  space  occupied  by  the 
body,  or  whether  it  be  all  concentrated  in  that  center  of  gravity. 

In  consequence  of  this  law  of  the  center  of  gravity,  the  reason- 
ings on  mechanical  subjects  are  often  greatly  simplified.     Thus,  in- 


46  MECHANICS. 

stead  of  estimating  the  pressure  and  other  mechanical  effects  of  a 
large  body  like  the  earth  by  considering  the  united  effects  of  all  its 
separate  parts,  we  rnay  often  arrive  at  a  far  more  simple  conclusion 
by  considering  all  the  matter  of  the  earth  as  residing  in  the  center 
of  gravity,  and  reasoning  respecting  it  accordingly.  When  bodies 
that  compose  a  system  are  in  motion,  their  common  center  of  gravity 
will  move  in  the  same  manner  as  if  a  body  equal  to  the  sum  of  the 
bodies  were  placed  in  that  point,  and  the  same  motions  were  commu- 
nicated to  it  as  are  communicated  to  the  bodies  separately. 

92.  Two  weights  or  pressures  acting  at  the  extremities  of  an  in- 
flexible rod  void  of  gravity,  will  be  in  equilibrium  about  a  given  point, 
when  their  distances  from  that  point  are  to  each  other  inversely  as 
those  weights  or  pressures. 

Thus,  (Fig.  17.)  if  a  weight      ^J  Fig.  17. 

of  one  pound,   and   another  of 
ten  pounds,  be  connected  by  a 
wire,   and    balanced   by  laying 
the  wire  across  a  thin  edge,  it  will  be  found  that  the  smaller  weight  is 
ten  times  as  far  from  the  support,  or  fulcrum,  as  the  larger  weight  is, 

93.  Whatever  be  the  form  or  dimensions  of  a  body  upon  a  plane 
parallel  to  the  horizon,  it  will  remain  at  rest,   if  the  line  drawn 
from  its  center  of  gravity  perpendicular  to  the  horizon  falls  within 

its  base. 

For  let  ABCD  FiS-  18- 

(Fig.    18.)   repre-       A  D  A  D 

sent  the  section 
of  a  body,  passing 
through  its  center 
of  gravity  G,  and 
draw  GF  perpen- 
dicular'fo  HO  the 


H  BF  C  F  B  C  0 

plane  upon  which 

it  stands ;  then,  since  the  tendency  of  the  body  to  descend  is  the 
same  as  if  its  whole  weight  were  concentrated  in  G,  it  will  rest 


CENTER    OP    GRAVITY. 


47 


or  fall  according  as  G  is  supported  or  not ;  i.  e.  according  as  F 
falls  within  or  without  the  base  BC ;  moreover,  the  stability  of  the 
body  will  depend  upon  the  distance  at  which  the  point  F  falls  with- 
in the  base.  i  »  ; 

94.  If  a  body  be  suspended  from  any  point,  it  will  not  rest  till  the 
line  which  joins  the  center  of  gravity  and  point  of  suspension  is  per- 
pendicular to  the  horizon. 

For  let  ABCD  (Fig.  19.)  represent  FiS-  19- 

the  section  of  a  body  as  before,  G  its 
center  of  gravity,  S  the  point  of  suspen- 
sion ;  join  SG,  and  draw  SOW  perpen- 
dicular to  the  horizon ;  produce  SG  to 
N,  and  draw  GR  parallel  to  SW ;  then, 
since  the  weight  of  the  body  may  be 
considered  as  collected  in  G,  its  tenden- 
cy to  motion  will  be  along  the  line  GR. 
Let  GR  therefore  represent  this  tenden- 
cy, which  resolve  into  GN  in  the  direc- 
tion SG,  and  RN  perpendicular  to  it ; 
the  part  GN  is  counteracted  by  the  reac- 
tion from  the  point  of  suspension  S,  and 

NR  is  employed  in  producing  motion  in  the  direction  of  the  circular 
arc  GO ;  G  therefore  (and  consequently  the  body)  will  not  remain 
at  rest  till  NR  vanishes,  i.  e.  till  the  angle  NGR  (=OSG)  vanishes, 
or  SG  coincides  with  SO. 

95.  When  a  body  is  suspended  from  a  center  of  motion,  and  re- 
volves around  it,  it  will  be  at  rest  only  when  the  center  of  gravity  is 
either  directly  below,  or  directly  above  the  center  of  motion.     For  it 
is  only  in  these  two  cases,  that  the  center  of  gravity  will  he  in  the 
line  which  is  drawn   through  the  center  of  motion  perpendicular  to 
the  horizon.     The  stationary  point  above  the  center  of  motion  is 
very  unstable,  since  the  slightest  disturbing  force,   throws  the  body 
out  of  the  line  of  direction,  when,  by  the  force  of  gravity,  it  imme- 
diately descends  to  the  lowest  point  it  can  reach,  and  vibrates  about 
that  point  until  it  finally  settles  itself  with  the  center  of  gravity  im- 
mediately under  the  point  of  suspension  ;  and  whenever  it  is  thrown 


48  MECHANICS. 

out  of  this  position,  the  same  vibrations  are  renewed  until  it  resumes 
it.  When,  therefore  the  center  of  gravity  is  at  the  lowest  point  it  is 
capable  of  reaching,  the  equilibrium  is  stable,  since  the  body  ob- 
stinately maintains  that  position.  On  this  principle,  gates  which 
have  their  center  of  gravity  raised  as  they  are  opened,  shut  spon- 
taneously. 

96.  The  stability  of  a  body  not  only  requires  that  the  center  of 
gravity  should  be  low,  but  that  the  line  of  direction  (or,  the  line 
which  is  drawn  through  the  center  of  gravity  perpendicular  to  the 
horizon)  should  fall  within  the  base.     The  farther  it  falls  from  the 
extremity  of  the  base,  the  more  stable  is  the  position.     Hence  the 
stability  of  a  pyramid  when  standing  on  its  broad  base,  and  its  insta- 
bility when  inverted.     For  the  same  reason,  all  broad  vessels,  as 
steam  boats,  are  difficult  to  upset,  while  vehicles  with  narrow  bases 
are   easily  overturned.     When  a  load  is  so  situated  as  to  raise  the 
center  of  gravity,  it  increases  the  liability  to  upset,  because  it  in- 
creases the  facility  with  which  the  line  of  direction  is  thrown  without 
the  base.     Thus  carts  loaded  with  hay,  or  bales  of  cotton,  are  very 
liable  to  be  overturned.     The  same  is  true  of  stages  carrying  pas- 
sengers or  baggage  on  the  top.     On  the  other  hand,   a  large  ship 
well  supplied  with  ballast  is  capsized  with  'great  difficulty,  since  the 
the  center  of  gravity  of  all  parts  of  the  ship  is  so  low,  as  to  render 
it  difficult  to  throw  the  line  of  direction  without  the  base.     Yet  if 
the  center  of  gravity  is  very  low,  a  ship  will  rock  excessively  in  a 
rough  sea,  since  the  upper  parts  near  the  deck,  move  over  a  great- 
er space  in  proportion  as  their  distance  from  the  center  of  gravity  is 
greater. 

97.  There  are  many  remarkable  structures  which  lean  or  incline 
a  little ;  but  so  long  as  the  line  of  direction  falls  within  the  base,  and 
the  parts  of  the  mass  have  sufficient  tenacity  among  themselves  to 
hold  together,  the  structure  will  stand.     The  famous  tower  of  Pisa, 
was  built  ^intentionally  inclining,  to  frighten  and  surprise :  with  a  height 
of  one  hundred  and  thirty  feet,  it  overhangs  its  base  sixteen  feet. 
This  circumstance  greatly  enhances  the  emotion  of  the  spectator  from 
its  summit.     Many  ancient  spires  and  other  tall  structures,  are  found 
to  have  lost  something  of  their  perpendicularity. 


CENTER    OF    GRAVITY.  49 

98.  Rocking  stones  are  rocks  which  are  sometimes  found  so  ex- 
actly poised  upon  their  center  of  gravity,  that  a  very  small  force  is 
sufficient  to  put  them  in  motion.     The  rocking  of  a  balloon  when  it 
begins  to  ascend,  affords  an  illustration  of  the  tendency  of  bodies  to 
vibrate  around  the  center  of  gravity. 

99.  The  motions  of  animals  are  regulated  in  conformity  with  the 
doctrines  of  the  center  of  gravity.     A  body  is  seen  tottering  in  pro- 
portion as  it  has  great  altitude  and  a  narrow  base  ;  but  it  is  a  pecu- 
liarity in  man  to  be  able  to  support  his  figure  with  great  firmness,  on 
a  very  narrow  base,  and  under  constant  changes  of  attitude.     The 
faculty  is  acquired  slowly,  because  of  the  difficulty.     The  great  fa- 
cility with  which  the  young  of  quadrupeds  walk,  is  ascribed  in  part 
to  their  broad  supporting  base.     Many  of  our  most  common  motions 
and  attitudes,  depend  for  their  ease  and  gracefulness,  upon  a  prop- 
er adjustment  of  the  center  of  gravity.     The  erect  posture  of  a  man 
carrying  a  load  upon  his  head — leaning  to  one  side  when  a  heavy 
weight  is  carried  in  the  opposite  hand — leaning  forward  when  a  weight 
is  on  the  back — or  backward  when  the  weight  is  in  the  arms ; — 
these  are  severally  examples  in  point.     When  a  man  rises  from  his 
chair,  he  brings  one  foot  back,  and  leans  the  body  forward,  in  order 
to  bring  the  center  of  gravity  over  the  base  ;  and  without  adjusting  it 
in  this  manner,  it  is  hardly  possible  to  rise.     A  man  standing  with 
his  heels  close  to  a  perpendicular  wall,  cannot  bend  forward  suffi- 
ciently to  pick  up  any  object  that  lies  on  the  ground  near  him,  with- 
out himself  falling  forward. 

100.  The  art  of  rope  or  wire  dancing,  depends  in  a  great  degree 
upon  a  skilful  adjustment  of  the  center  of  gravity.     The  rope  dan- 
cer frequently  carries  in  his  hand  a  stick  loaded  with  lead,  which' 
he  so  manages  as  to  counterbalance  the  inclinations  of  his  body  which 
would  throw  the  line  of  direction  out  of  the  base.     Upon  a  similar 
principle  the  equestrian  balances  himself  on  one  foot  on  a  galloping 
horse. 

101.  The  vegetable  creation  is  subject  also  to  these  general  laws 
of  nature.     Trees  by  the  weight  and  height  of  their  tops  would  seem* 
peculiarly  liable  to  fall ;  but  their  roots  afford  a  corresponding  breadtfo 


50  MECHANICS. 

of  base,  while  their  perpendicular  trunks,  and  the  symmetrical  dispo- 
sition of  the  branches,  conspire  to  increase  their  stability. 

102.  The  position  of  the  center  of  gravity  of  any  number  of  sep- 
arate'bodies,  is  never  altered  by  the  mutual  action  of  those  bodies 
on  each  other.     If,  for  example,  two  bodies,  by  mutual  attraction, 
approach  each  other,   the  center  of  gravity  remains  at  rest,  until 
finally  the  bodies  meet  in  this  point.     If,  by  their  mutual  action,  they 
contribute  to  make  each  other  revolve  in  orbits,   it  is  around  their 
common  center  of  gravity.     Thus  the  earth  and  moon  revolve  around 
a  common  center  of  gravity,  which  remains  fixed  :  the  same  is  true 
of  the  sun  and  all  the  bodies  that  compose  the  solar  system.     Were 
the  centrifugal  force  to  be  suspended,   and  the  bodies  abandoned  to 
the  mutual  action  of  each  other,  they  would  all  meet  in  their 'common 
center  of  gravity.     This  naturally  results  from  the  principle  that  the 
momenta  on  opposite  sides  of  the  center  of  gravity  are  equal,  and  that 
bodies  by  their  mutual  action  produce  equal  momenta  in  each  other. 

103.  The  doctrines  of  the  center  of  gravity,  suggest  the  readiest 
method  of  solving  a  great  number  of  practical  problems.     We  an- 
nex a  single  example. 

Suppose  three  persons  were  carrying  a  stick  of  timber,  (A  by  him- 
self supporting  one  end,  and  B  and  C  by  a  handspike  lifting  together 
towards  the  other  end,)  and  it  were  required  to  determine  at  what 
distance  from  the  end  of  the  stick  the  handspike  must  be  placed,  in 
order  that  three  persons  might  bear  equally. — A  stick  of  timber 
being  a  body  of  regular  shape  and  uniform  density,  has  its  center  of 
'  gravity  coincident  with  the  center  of  magnitude.  We  may  therefore 
proceed  on  the  supposition  that  the  entire  weight  is  collected  in  the 
center.  Now  in  order  that  B  and  C  may  together  lift  twice  as  much 
as  A,  they  must  be  twice  as  near  the  center.  But  the  distance  of  A 
from  the  center  is  half  the  length  of  the  stick ;  therefore  the  distance 
of  the  reqnired  point  from  the  center  is  one  fourth  the  length  of  the 
stick,  and  consequently  it  is  one  fourth  the  same  length  from  the  end 
of  the  stick.  To  test  this  case  by  experiment,  we  might  rest  one  end 
of  the  stick  upon  a  support,  and  ascertain,  by  a  pair  of  steelyards,  the 
weight  at  a  distance  from  the  other  end  equal  to  J  the  length  of  the 
sti  ck.  It  would  be  found  equal  to  |  the  weight  of  the  whole  stick, 


PROJECTILES    AND    GUNNERY.  51 

CHAPTER  VII. 

OF  PROJECTILES  AND  GUNNERY. 

104.  A  projectile,  is  any  body  thrown  into  the  atmosphere.     A  ball 
fired  from  a  cannon,  a  stone  thrown  by  the  hand,  and  an  arrow  shot 
from  a  bow,  are  severally  examples  of  projectiles.     According  to 
article  83,  projectiles  rise  and  fall  in  the  curve  of  a  parabola  under 
the  combined  forces  of  projection,  which  tends  to  carry  them  uni- 
formly forward,  and  of  gravity,  which  brings  them  with  accelerated 
velocity  towards  the  earth. 

105.  The  random  of  a  projectile  is  the  horizontal  distance  between 
the  point  from  which  it  is  thrown,  and  that  where  it  falls  to  the  earth. 

For  example,  when  I  throw  a  stone  obliquely  into  the  air,  it  rises 
and  falls  in  a  curve,  (the  parabola)  and  the  distance  from  the  place 
where  I  stand  to  the  place  where  it  falls,  measured  on  the  surface  of 
the  earth,  is  its  random.  The  random  is  greatest  when  the  angle  of 
elevation  is  45  degrees,  and  is  the  same  at  elevations  equally  distant 
above  and  below  45  degrees.  It  is  the  same,  for  instance,  at  60  and 
at  30  degrees. 

A  projectile  rises  to  the  greatest  height  when  thrown  perpendicu- 
larly upwards,  and  it  remains,  in  this  case,  longest  in  the  air ;  or  the 
time  of  flight  is  greatest  when  a  body  is  projected  directly  upwards. 

106.  When  a  body  is  thrown  horizontally  from  any  elevation,  with 
a  velocity  equal  to  that  which  it  would  have  acquired  by  falling  from 
that  elevation  to  the  earth,  its  random  is  twice  as  great  as  that  height. 
Thus,  if  I  throw  a  ball  from  a  chamber  window,  with  a  velocity 
which  it  would  have  acquired  in  falling  from  the  window  to  the 
ground,  it  will  fall  at  a  distance  from  the  foot  of  the  building  equal ' 
to  twice  the  height  of  the  window. 

107.  The  foregoing  principles  hold  good  only  when  projectiles 
move  without  resistance.     But  this  is  far  from  being  the  fact,  since 
the  resistance  of  the  air,  especially  to  bodies  moving  swiftly  through 
it,  is  very  great ;  and  hence  the  discordance  between  theory  and 
experiment  is  such,  that  the  mathematical  principles  of  projectiles 
are  found  to  be  wholly  inapplicable  to  practice. 


52  MECHANICS. 

It  is  ascertained,  in  general,  that  projectiles  moving  slowly,  des- 
cribe curves  which  are  nearly  parabolas ;  while  such  as  move  swiftly 
deviate  very  far  from  this  curve.  The  parabolic  figure  described 
in  the  case  of  projectiles  which  move  slowly,  may  be  observed  in 
tracing  the  path  of  a  small  stone  thrown  into  the  air,  and  more  espe- 
cially in  the  curves  described  by  jets  of  water  spouting  upwards,  as 
in  fountains.  But  when  the  jet  is  more  rapid,  and  spouts  at  a  high 
angle,  as  forty  five  degrees  for  example,  we  can  plainly  see  that  the 
curve  deviates  greatly  from  a  parabola.  The  remote  branch  of  the 
curve  is  seen  to  be  much  less  sloping  than  the  rising  branch ;  and  in 
very  great  jets,  which  are  to  be  seen  in  some  great  water  works,  the 
falling  branch  is  almost  perpendicular  at  its  remote  extremity ;  and 
the  highest  point  of  the  curve  is  far  from  being  in  the  middle  between 
the  spout  and  the  place  where  the  water  falls.  The  unequal  division 
of  the  curve  by  its  highest  point,  may  also  be  observed  in  the  flight 
4of  an  arrow  or  a  bomb  shell. 

108.  The  following  facts  also  shew  the  discordance  between  the 
parabolic  theory  of  gunnery  and  experience.  A  cannon  ball,  fired 
in  such  a  direction  and  with  such  a  velocity,  that  its  random  or  hori- 
zontal range,  ought  to  be  twenty  four  miles,  comes  to  the  ground 
short  of  one  mile.  The  times  of  rising  and  falling,  if  that  theory 
held  good,  ought  to  be  equal ;  but  the  time  of  rising  is  greater  than 
that  of  falling  at  great  elevations,  and  at  small  elevations,  less  than 
that  of  falling.  According  to  the  theory,  the  greatest  random,  is  at 
an  angle  of  elevation  of  forty  five  degrees,  but  in  practice  it  is  found 
to  be  much  below  this.  The  greatest  random  of  an  arrow,  is  when 
the  elevation  is  about  thirty  six  or  thirty  eight  degrees.  Indeed  the 
angle  for  the  greatest  horizontal  range,  may  be  at  all  degrees  from 
45°  to  30°  ;  the  slowest  motions  and  the  largest  shot  being  almost  at 
45°,  but  gradually  more  and  more  below  that  degree  as  the  shot  is 
smaller  and  the  velocity  is  greater,  till  at  length  with  the  most  rapid 
motions,  and  the  smallest  shot,  the  angle  is  little  above  30°.  The 
following 'Experiments  were  made  in  France  by  Borda,  with  a  twenty 
four  pounder,  with  the  same  charge  of  powder  in  each  experiment. 


PROJECTILES    AND     GUNNERY.  53 

Elevation.  Range. 

15°  1950 

30       -  -       2235 

45  2108 

60 1700 

•      75 -       950 

Whence  it  appears  that  at  the  elevations  of  15°  and  75°,  the  ran- 
doms instead  of  being  the  same  (being  equally  distant  from  45,)  were  as 
the  numbers  1950  and  950. 

109.  All  this  discordance  between  theory  and  practice  is  owing  to 
the  resistance  of  the  air,  which,  when  the  projectile  moves  with 
great  velocity,  becomes  enormous.     Nor  will  it  be  difficult,  on  a  lit- 
tle reflection,  to  comprehend  the  reason  why  this  resistance  should 
be  so  great.     The  force  with  which  a  projectile  strikes  the  air 
at  rest,  is  the  same  as  that  with  which  the  air  moving  with  equal 
velocity  would  strike  the  body  at  rest.     This,  in  the  case  of  a  can- 
non ball,  would  greatly  exceed  the  most  violent  hurricane.     Again, 
as  a  ball  moves  through  the  air,  it  displaces,  that  is,  gives  mo- 
tion to,  great  quantities  of  air ;  yet  whatever  motion  it  imparts  to 
other  bodies  is  extinguished  in  itself.     The  loss  of  motion,  there- 
fore, increases  very  fast  with  the  velocity.     It  is  said  to  be  in  gen- 
eral as  the  square  of  the  velocity  :  so  that  a  body  moving  through 
the  air  with  ten  limes  the  velocity  of  another  body,  would  encounter 
one  hundred  times  as  much  resistance.     In  very  swift  motions,  the 
resistance  was  ascertained  by  Robins  to  be  even  much  greater  than 
in  the  ratio  of  the  square  of  the  velocity. 

110.  The  researches  of  Mr.  Robins  were  made  chiefly  by  the 
aid  of  an  instrument  of  his  own  invention,  called  the  Ballistic  Pen- 
dulum.    It  consists  of  little  more  than  a  large  block  of  wood,  like  a 
log,  suspended  after  the  manner  of  a  pendulum.     Now  if  a  bullet  be 
tired  into  the  block,  as  the  bullet  will  be  stopped,  and  as  it  imparts  to 
the  block  whatever  motion  it  loses,  consequently  the  momentum  of  the 
block  after  the  stroke,  is  precisely  that  of  the  ball  before  the  stroke. 
Hence  the  weight  of  the  block  -and  that  of  the  ball  being  known, 
and  the  velocity  imparted  to  the  block  being  easily  determined  by 
observation,  it  is  easy  to  find  the  velocity  of  the  ball ;  for  the  weight 
of  the  ball  is  to  the  weight  of  the  block,  as  the  velocity  of  the  block 
is  to  the  velocity  of  the  ball. 


MECHANICS. 

111.  This  simple  apparatus  is  sufficient  for  ascertaining  a  great 
number  of  particulars  relative  to  the  art  of  gunnery.     If  the  ball  is 
fired  nearly  in  contact  with  the  block,  we  find  with  what  velocity  it 
leaves  the  gun;  if  at  different  distances  from  the  block,  we  find 
how  much  the  velocity  is  retarded  by  passing  through  the  air,  for 
those  distances  respectively.     If,  at  a  given  distance,  we  vary  the 
charge  of  powder,  we  find  the  respective  changes  which  the  velocity 
undergoes,   and  hence  learn  the  ratio  that  ought  to  be  observed  be- 
tween the  powder  and  the  ball,  in  order  to  produce  the  maximum 
effect.     The  effects  resulting  from  variations  in  the  length,  shape  and 
bore  of  the  gun,  are  also  ascertained  with  equal  facility. 

112.  The  following  are  some  of  the  practical  results  ascertained 
by  the  experiments  of  Mr.  Robins,  Count  Rumford,  and  Dr.  Hut- 
ton.     A  musket  ball,  discharged  with  a  common  charge  of  powder, 
issues  from  the  muzzle  of  the  piece  with  a  velocity  between  1600 
and  1700  feet  in  a  second.     The  utmost  velocity  that  can  be  given 
Co  a  cannon  ball  is  2000  feet  per  second,  and  this  it  has  only  at  the 
moment  of  leaving  the  gun.     In  order  to  increase  the  velocity  from 
1600  to  2000  it  requires  half  as  much  more  powder,  which  involves 
a  hazardous  strain  upon  the  gun,  and  the  velocity  will  be  reduced  to 
1300  before  the  ball  has  proceeded  500  yards. 

113.  From  the  foregoing  considerations  it  is  inferred  that  great 
charges  of  powder  are  absolutely  useless  in  the  service  of  artillery, 
especially  when  the  distance  of  the  object  is  considerable,  and  that  a 
velocity  exceeding  1100  should  not  be  aimed  at.     The  maximum 
service  charge  is  f  the  weight  of  the  ball.     In  close  naval  engage- 
ments, great  velocities  are  injurious,  for  the  ball  may  then  pass  through 
both  sides  of  the  vessel  without  lodging,  and  the  number  of  splinters 
produced  by  a  ball  in  rapid  motion,  is  much  less  than  is  caused  by 
one  moving  more  slowly.     By  reducing  the  charge  we  may  also  re- 
duce the  size  and  strength  of  the  gun ;  and  hence  guns  are  made  of 
smaller  dimensions  now  than  formerly,  in  order  to  do  the  same  exe- 
cution.    The  velocity  with  which  a  charge  of  powder  expands  itself 
at  first,  is  estimated  by  Hutton  as  high  as  5000  feet  per  second.     As 
it  expands,  this  velocity  is  of  course  constantly  diminishing,  but  will 
exceed  that  of  the  ball  while  the  latter  is  passing  through  the  barrel 


PROJECTILES    AND    GUNNERY.  55 

of  the  gun,  and  will  act  as  a  constantly  accelerating  force.  Long 
guns,  therefore,  give  to  balls  a  greater  velocity  than  short  ones ;  but 
the  gain  secured  in  this  way  after  a  moderate  length  is  so  small, 
(there  being  also  some  disadvantages  peculiar  to  long  guns,)  that 
cannon  have  of  late  years  been  much  shortened.  In  the  naval  ser- 
vice, carronades  have  been  introduced.  These  are  a  short  kind  of 
gun,  with  small  bore,  requiring  for  a  charge  of  powder,  only  one 
twelfth  the  weight  of  the  ball.  Their  weight  and  thickness  are  pro- 
portionally reduced,  yet  in  close  action  they  produce  effects  superior 
to  those  of  long  guns. 

114.  It  has  been  found  that  no  difference  is  caused  in  the  velocity, 
or  range,  by  varying  the  weight  of  the  gun,  nor  by  the  use  of  wads, 
nor  by  different  degrees  of  ramming,  nor  by  firing  the  charge  of 
powder  in  several  places  at  the  same  time ;  but  that  a  very  great 
difference  in  the  velocity  arises  from  a  small  degree  in  the  windage, 
or  the  difference  between  the  diameter  of  the  ball  and  that  of  the  gun. 
Indeed,  with  the  usual  established  windage  only,  viz.  about  aV  of  the 
calibre,  no  less  than  between  J  and  J  of  the  powder  escapes  and  Is 
lost,  and  as  the  balls  are  often  smaller  than  the  regulated  size,  it  fre- 
quently happens  that  half  the  powder  is  lost  by  unnecessary  windage. 
To  this  cause  also,  namely,  too  great  windage,  Dr.  Hutton  ascribes 
a  great  part  of  the  sideways  deviation  of  a  ball ;  since  when,  in  pass- 
ing through  the  barrel  of  the  gun,  it  is  knocked  from  side  to  side,  ft 
will  finally  take  the  last  direction  which  it  happened  to  have  at  the 
muzzle  of  the  gun.     Another  cause  of  this  deviation  from  the  line 
of  direction,  arises  from  a  want  of  perfect  sphericity  in  the  ball,  by 
which  means  the  two  sides  do  not  meet  with  equal  resistance.     Ri- 
fles owe  their  superiority  over  common  guns,  chiefly  to  their  obvia- 
ting this  deviation.     They  have  a  spiral  groove  cut  in  their  bore, 
making  about  a  turn  and  a  half  in  the  whole  length  of  the  barrel. 
The  ball,  which  is  made  to  fit  close  to  avoid  too  great  windage,  has 
a  corresponding  motion  impressed  on  it,  which  it  retains  after  it 'leaves 
the  gun,  continuing  to  revolve  around  the  line  of  direction.     What- 
ever inequalities,  may  exist  in  the  ball,  their  effects  are  neutralized, 
by  their  being  first  on  one  side  and  then  on  the  other  of  this  line. 

115.  When  a  ball  is  projected   from  a  piece  of  ordnance,  at  a 
small  angle  of  elevation,  and  falls  upon  water,  or  on  a  plane  of  hard 


MECHANICS. 


earth,  its  flight  will  not  cease,  but  it  will  rise  again  and  .describe  a 
second  curve,  similar  to  the  first  but  less  ;  and  it  will  continue  to 
rebound,  until  the  whole  of  its  projectile  velocity  is  destroyed. 
This  species  of  firing  is  called  Ricochet.  It  is  applied  with  great 
advantage  from  sea  coast  batteries  upon  shipping,  and  in  the  attack  of 
fortresses.  The  pieces  are  fired  with  small  charges  of  powder  and 
elevated  only  from  3  to  6  degrees.  The  word  signifies  duck  and 
drake,  or  rebounding  ;  because  the  ball  or  shot  thus  discharged,  goes 
bounding  and  rolling  along,  killing  or  destroying  every  thing  in  its 
way,  like  the  bounding  of  a  flat  stone  along  the  surface  of  water 
when  thrown  almost  horizontally. 


CHAPTER  VIII. 

OF  MACHINERY.— THE  LEVER. 

116.  THE  organs  employed  in  communicating  motion,  are  tools, 
machines,  and  engines.  Tools  are  the  simplest  instruments  of  art ; 
these  when  complicated  in  their  structure,  become  machines;  and 
machines  when  they  act  with  great  power,. take  the  name  of  engines. 
Among  the  ancients,  machines  were  confined  chiefly  to  the  purposes 
of  architecture  and  war  ;  and  they  were  moved  almost  exclusively 
by  the  strength  of  animals.  Thus,  in  building  one  of  the  great 
Pyramids  of  Egypt,  vast  masses  of  stones  were  raised  to  a  great 
height,  amounting  together  to  10,400,000  tons.  In  this  labor  were 
employed  100,000  men  for  twenty  years.  The  advantage  which 
man  has  gained  by  pressing  into  his  service  the  great  powers  of  na- 
ture, instead  of  depending  on  his  own  feeble  arm,  is  evinced  by  the 
fact,  that  by  the  aid  of  the  steam  engine,  one  man  can  now  accom- 
plish as  much  labor  as  27,000  Egyptians,  working  at  the  rate  at 
which  they  built  the  pyramids.  In  war  also,  while  the  use  of  gun- 
powder was  unknown,  engines  of  great  power  were  invented  for 
throwing  stones  and  javelins,  and  for  demolishing  fortifications.  Such 
were  the'jCatapulta,  the  Ballista,  and  the  Battering  Ram,  of  the 
Romans.  Yet  it  is  remarkable,  that  during  many  ages,  while  such 
powerful  auxiliaries  were  employed  in  architecture  and  in  war,  the 
ancients  should  have  made  so  little  use  as  they  did  of  machinery  in 
the  ordinary  processes  of  the  arts.  The  practice  of  grinding  corn  by 


MACHINERY.  57 

hand,  which  was  chiefly  performed  by  women,  was  prevalent  at  Rome 
until  the  time  of  Augustus,  when  we  find  the  first  mention  of  water  mills. 
The  elements  of  machinery  are  found  in  what  are  called  the  Me- 
chanical Powers.  They  are  six  in  number,  viz.  the  Lever,  the  Wheel 
and  Axle,  the  Pulley,  the  Inclined  Plane,  the  Screw,  and  the  Wedge. 

THE    LEVER. 

117.  1.   The  LEVER  is  an  inflexible  bar  or  rod,  some  point  oj 
which  being  supported,  the  rod  itself  is  movable  freely  about  that 
point,  as  a  center  of  motion. 

2.  This  center  of  motion  is  called  the  FULCRUM  OR  PROP. 

3.  Wtien  two  forces  act  on  one  another  by  means  of  any  machine, 
that  which  gives  motion  is  called  the  POWER  ;  that  which  receives  it  the 

WEIGHT. 

4.  A  lever  is  straight  when  its  arms  (or  the  parts  on  each  side  of 
the  fulcrum)  are  in  one  continued  straight  line ;  bent,  when  the  two  arms 
are  straight,  but  make  any  angle  with  each  other  at  the  center  of  mo- 
tion ;  and  crooked,  when  one  or  both  arms  deviate  from  a  straight  line. 

118.  In   treating  of  the  Mechanical  Powers,  the  first  inquiry  is, 
what  are  the  conditions  of  an  equilibrium;  that  is,  when  do  the  pow- 
er and  weight  exactly  balance  each  other  ?  This  point  being  ascer- 
tained, any  addition  to  the  power,  puts  the  weight  in  motion.     The 
investigation  first  proceeds  on  the  supposition  that  the  action  of  the 
mechanical  powers  is  not  impeded  by  their  own  weight,  or  by  fric- 
tion and  resistance,  a  suitable  allowance  being  afterwards  made  for 
the  various  impediments. 

119.  The  following  principles  are  regarded  as  self-evident. 

Axiom  1 .  If  two  weights  balance  each  other  upon  the  opposite  arms 
of  a  straight  lever,  the  pressure  upon  the  fulcrum  is  equal  to  the 
sum  of  the  weights,  whatever  be  the  length  of  the  lever. 

Ax.  2.  If  a  weight  be  supported  on  a  lever  which  rests  on  twoful- 
crums,  the  pressure  upon  the  fulcrum  is  equal  to  the  whole  weight. 

Ax.  3.  Equal  forces  acting  perpendicularly  at  the  extremities  of 
equal  arms  of  a  lever,  exert  the  same  effort  to  turn  the  lever  round. 

120.  Two  weights  will  balance  each  other  upon  the  arms  of  a  lever 
when  they  are  to  each  other  inversely  as  their  respective  distances  from 
the  fulcrum.  8 


58 


MECHANICS. 


1 


1 


Thus  in   Fig.  20,  if       A Fig.  20.    c 

W  is  as  much  heavier 

than  P  as  AC  is  greater 

than  BC,  the  two  weights      j^  ^  W 

will  exactly  balance  one 

another.     Here  the  product  of  P  jnto  AC,  is  equal  to  the  product  of 

W  into  BC,  and  in  all  cases  where  the  product  of  the  weight  into  its 

distance  from  the  fulcrum,  is  equal  to  the  product  of  the  power  into 

its  distance  ;  the  weight  and  the  power  will  be  in  equilibrium.     This 

is  true  even  where  there  are  several  weights  on.  each  side  as  in 

figure  21.     If  the  products  of  A  and  B  into  their  respective  distan- 


Fig. 21. 


D 


G 


ces  from  G,  be  equal  to  the 
similar  products  of  C  and  D, 
the  weights  on  the  opposite 
sides  will  balance  on  another. 

121.  Levers  are  divided  into 
three  different  orders,  accord- 
ing to  the  position  of  the  pow- 
er and  weight  with  respect  to 
the  fulcrum. 

1.  In   a  lever  of  the  first 
kind  the  fulcrum  is  between 
the  power  and  the  weight,  as 
in  Fig.  20. 

2.  In  a  lever  of  the  second 
kind,  the  weight  is  applied  be- 
tween the  power  and  the  ful- 
crum, as  in  Fig.  22. 

3.  In  a*lever  of  the  third 
kind  the  power  is  applied  be- 
tween the  weight  and  the  ful- 
crum, as  in  Fig.  23. 


Fig.  22. 


C                     B 

r   T 

A 

Fig>  23. 


MACHINERY.  59 

The  same  law  of  equilibrium  (Art.  120.)  holds  good  in  the  three 
kinds  of  levers ;  and  where  the  power  is  at  a  greater  distance  from 
the  fulcrum  than  the  weight,  as  in  the  first  and  second  kinds,  it  is 
proportionally  less  than  the  weight,  and  where  it  is  nearer  the  fulcrum 
than  the  weight,  as  in  the  third  kind,  it  is  proportionally  greater  than 
the  weight,  or  acts  under  what  is  called  a  mechanical  disadvantage. 

122.  When  levers  are  not  straight,  but  more  or  less  crooked,  a  sim- 
ilar principle  of  equilibrium  holds  good,  the  distance  of  the  weight  or 
power  from  the  fulcrum  being  estimated  by  the  length  of  a  perpendicu- 
lar drawn  from  the  fulcrum  to  the  line  of  direction  in  which  the  power 
acts.  Thus  in  figure  24,  ABC  is  a  crooked  lever,  in  which  the  power 


Fig.  24. 


and  weight  act  in  the  directions  of  the  lines  BS  and  AS.  Now  the 
distances  from  the  fulcrum  being  measured  by  the  perpendiculars 
CM  and  CN,  the  general  law  of  equilibrium  holds,  viz.  that  the  pow- 
er is  to  the  weight,  as  the  distance  of  the  weight  from  the  fulcrum  is 
to  the  distance  of  the  power  from  the  fulcrum. 

123.  A  compound  lever  consists  of  several  simple  levers  combin- 
ed together. 

In  a  compound  lever,  the  power  arid  the  weight  balance  each 
other,  when  the  product  of  the  power  multiplied  into  all  the  arms  on 
the  side  next  to  it,  is  equal  to  the  product  of  the  weight  into  all  the 
arms  next  to  the  weight. 


60 


MECHANICS. 

Fig.  25. 

Q 

A 

oj 

G      E 

w 


Thus,  in  figure  25,  the  product  of  P  X  AC  XBF  xDG=W  X  GE 
X  FD  X  CB.  Suppose,  for  example,  the  longer  arms  of  the  lever 
are  severally  twice  the  length  of  the  shorter,  and  that  the  weight  to 
be  raised  equals  400  pounds ;  what  power  must  we  apply  ?  1  X  1  X 
1  X400 =2X2X2X50.  Hence,  50  Ibs.  applied  at  P  would  bal- 
ance 400  Ibs.  at  W. 

124.  Examples. 

1.  Upon  the  extremities  of  a  straight  lever,  are  hung  two  weights, 
A  and  B,  the  former  weighing  15  and  the  latter  60  pounds;  how 
much  farther  is  A  from  the  fulcrifm  than  B  ?     By  figure  20,  AC  : 
CB:  :60  :  15;  but  60  :  15:  :4  :  1 ;  therefore,  the  smaller  weight  is 
four  times  as  far  from  the  fulcrum  as  the  larger. 

2.  One  end  of  a  lever  is  44  feet,  ,and  the  other  5  feet;  what 
power  must  I  apply  to  the  longer  end  to  balance  a  weight  at  the 
shorter  end  of  500  Ibs.  ? 

5x500 
44  :  5::500  :      44     =56  Ibs.  13T'Toz.  Ans. 

3.  In  a  compound  lever,  (Fig.  25.)  the  lengths  of  the  longer  arms 
are  5,  10,  16  feet,  respectively,  and  of  the  shorter  1,  2,  3  feet;  what 
power,  applied  to  the  longer  side,  will  be  required  to  balance  a  weight 
of  100  pounds?  5X10X16  :  Ix2x3::100  :  f  Ib.  Ans. 

4.  Wishing  to  lift  from  its  bed  a  rock  weighing  1000  Ibs.,  I  take 
a  handspike  6  feet  long,   and  applying  the  shorter  end  to  the  rock, 
rest  it  on  a  fulcrum  at  the  distance  of  Ij  feet  from  the  rock;  how 
much  force  must  I  exert  at  the  end  of  the  longer  arm  to  raise  the 
rock?  Ans.  333 J  Ibs.* 

*  This  force  would  just  balance  the  weight ;  any  additional  force 
would  raise  it. 


MACHINERY. 


61 


5.  A  lever  of  the  second  order  is  20  feet  long  :  at  what  distance 
from  the  fulcrum  must  a  weight  of  112  Ibs.  be  placed,  so  that  it  may 
be  supported  by  a  power  able  to  sustain  50  Ibs.  acting  at  the  ex- 
tremity of  the  lever?  Ans.  8  feet  and  11}  inches. 

6.  In  a  compound  lever,  the  three  shorter  arms  are,  respectively, 
1,  2,  4  feet;  the  three  longer  arms  9,  11,  12;  the  power  applied  at 
the  end  of  the  longer  arm  is  3  pounds :  what  weight  will  it  raise  ? 

Ans.  445J  Ibs. 

125.  The  principle  of  the  lever,  has  a  most  extensive  application 
in  the  arts,  and  the  forms  under  which  it  occurs  are  very  various. 
We  may  contemplate  it  as  having  equal  or  unequal  arms. 

The  balance  affords  the  most  common  example  of  a  lever  with 
equal  arms.  The  necessity  of  arriving  at  the  weight  of  bodies  with 
the  greatest  degree  of  accuracy  in  pecuniary  transactions,  and  more 
especially  in  delicate  scientific  researches,  as  those  of  chemical  anal- 
ysis, has  induced  men  of  science,  and^artists,  to  bestow  great  and 
united  attention  upon  the  construction  of  this  instrument,  until  they 
have  brought  it  to  an  astonishing  degree  of  perfection. 


Fig.  26. 


126.  The  princi- 
pal parts  of  the  bal- 
ance are  the  beam 
GH  (Fig.  26.)  the 
points  of  suspen- 
sions G  and  H,  and 
the  fulcrum  F.  In 
order  to  construct  a 
perfect  balance,  the 
most  important  par- 
ticulars to  be  at- 
tended to,  are  the 
length  of  the  arms, 
that  is,  of  the  beam; 
the  situation  of  the  center  of  gravity  of  the  whole  instrument,  with 
respect  to  the  fulcrum  or  center  of  motion ;  and  the  position  of  the 
point  of  suspension. 


62  MECHANICS. 

(1.)  The  sensibility  of  the  balance  is  increased  by  increasing  the 
lengths  of  the  arms;  but  unless  the  arms,  when  long,  are  at  the  same 
time  of  considerable  weight,  they  will  not  have  the  requisite  strength, 
but  will  be  liable  to  bend ;  and  an  increase  of  weight,  adds  to  the 
amount  of  friction  on  the  center  of  motion.  It  is  not  common  there- 
fore to  make  the  arms  of  a  very  delicate  balance  more  than  nine 
inches  in  length ;  and,  for  the  purpose  of  uniting  lightness  with 
strength,  the  beam  is  composed  of  two  hollow  cones  placed  base  to 
base,  as  in  Fig.  26. 

(2.)  The  center  of  gravity  of  the  instrument,  must  be  a  little  be- 
low the  center  of  motion.  For  if  the  beam  is  balanced  on  its  cen- 
ter of  gravity,  it  will  remain  at  rest  in  every  position,  whereas  it  must 
be  at  rest,  only  when  in  a  horizontal  position.  If  the  center  of  grav- 
ity is  above  the  center  of  motion,  the  position  is  too  unstable,  and 
on  the  least  disturbance  of  the  equilibrium,  the  beam  will  be  liable 
to  upset.  Finally  if  the  center  of  gravity  is  too  far  below  the  cen- 
ter of  motion,  the  equilibrium  will  be  too  stable.  Hence,  in  very 
delicate  balances,  the  center  of  motion  is  placed  a  little  above  the 
center  of  gravity. 

(3.)  The  points  of  suspension  must  be  in  the  same  right  line  with 
the  center  of  motion.  For  since  when  weights  are  added  to  the 
scales,  the  effect  is  the  same  as  though  they  were  concentrated  in 
the  points  of  suspension ;  and  were  those  points  above  the  center  of 
motion,  the  center  of  gravity  would  be  liable  to  be  shifted  above  the 
center  of  motion,  when  the  beam  would  upset ;  and  if  the  same 
points  were  below  the  center  of  motion,  unless  the  weights  added 
were  large,  the  center  of  gravity  would  be  too  low,  and  the  equi- 
librium too  stable. 

127.  In  order  to  prevent  friction  as  much  as  possible,  the  fulcrum 
is  made  of  hardened  steel,  and  shaped  into  a  triangular  prism,  or 
knife  edge,  smoothly  rounded,  and  turning  on  a  plane  of  agate  or 
steel,  or  some  othervery  hard  and  polished  substance. 

It  is.^nly  by  a  nice  attention  to  all  these  particulars  that  artists  have 
been  able  to  give  to  the  balance  so  great  a  sensibility.  Some  balances 
have  been  made  to  turn  with  the  1000th  part  of  a  grain.  By  loading 


MACHINERY.  63 

the  beam  the  sensibility  of  the  instrument  is  diminished ;  (Art.  124.) 
it  is  customary,  therefore,  to  estimate  its  power  by  finding  what  part 
of  the  weight  with  which  it  is  loaded  it  takes  to  turn  it.  Thus,  if 
when  loaded  with  7000  grains,  it  will  turn  with  1  grain,  its  power 
is  T^7.  A  balance  constructed  by  Ramsden,  a  celebrated  English 
artist,  for  the  Royal  Society,  turned  with  the  ten  millionth  part  of 
the  weight.  Delicate  balances  are  usually  covered  with  a  glass  case 
to  prevent  agitation  from  the  air,  and  to  secure  them  from  injury. 
Figure  26.  represents  an  instrument  of  this  kind  made  for  the  Royal 
Institution  of  Great  Britain. 

128.  The  bent  lever  balance  is  represented  in  figure  27.     The 
weight  C  acts  as  though  it  were  concentra- 
ted in  the  point  D,  and  the  weight  in  the 

scale  acts  at  K ;  hence  an  equilibrium  will 
take  place,  when  the  article  weighed  has  to 
C  the  same  ratio  as  DB  has  to  BK.  Now 
every  increase  of  weight  added  to  the  scales 
causes  C  to  rise  on  the  arc  F  G,  and  D  to 
recede  from  B.  Hence  the  different  posi- 
tions of  C,  according  as  different  weights 
are  added  to  the  scale,  may  be  easily  de- 
termined, and  the  corresponding  numbers 
marked  on  the  scale  F  G. 

129.  It  is  essential  to  an  accurate  balance,  that  the  two  arms 
should  be  precisely  equal  in  length.     The  false  balance,  which  is 
sometimes  used  with  a  design  to  defraud,  has  its  arms  unequal.     The 
dealer  turns  such  an  instrument  to  his  account  both  in  buying  and 
selling.     In  buying,  he  puts  his  weights  on  the  longer  side,  for  then 
it  takes  more  than  an  equivalent  to  balance  them  ;  and,  in  selling,  he 
puts  his  weights  on  the  shorter  side,  because  less  than  an  equivalent 
will  produce  an  equilibrium.     The  fraud  may  be  detected  by  ma- 
king the  weights  and  the  merchandize  change  places.     The  true 
weight  may  be  determined  from  such  a  balance,  by  putting  the  arti- 
cle whose  weight  is  to  be  determined,  into  one  scale,  and  counter- 
poising it  with  sand,  shot,  or  any  convenient  substance,  in  the  other 
scale,  and  then,  removing  the  article,  and  finding  the  exact  weight 


64  MECHANICS. 

of  the  counterpoise.  It  is  evident  that  the  weight  of  the  merchan- 
dize will  be  the  same  as  that  of  the  weights  employed  to  balance  its 
counterpoise. 

130.  The  steelyard  is  a  lever  having  unequal  arms,  in  which  the 
same  body  is  made  to  indicate  different  weights,  by  placing  it  at  dif- 
ferent distances  from  the  fulcrum.     A  pair  of  steelyards  has  usual- 
ly two  graduated  sides  for  determining  smaller  or  greater  weights. 
It  will  be  seen  that  on  the  greater  side,  the  weight  is  placed  nearer 
the  fulcrum.     Consequently,  the  weight  indicated  by  the  counter- 
poise, when  at  a  given  distance  from  the  fulcrum,  will  be  proportion- 
ally greater.     This  instrument  is  very  convenient  because  it  requires 
but  one  weight.     The  pressure  on  the  fulcrum,  excepting  that  of  the 
apparatus  itself,  is  only  that  of  the  article  weighed,  whereas  in  the 
balance,  the  fulcrum  sustains  a  double  weight.     But  the  balance  is 
susceptible  of  more  sensibility  than  the  steelyard,  because  the  sub- 
divisions of  its  weights  can  be  effected  with  a  greater  degree  of  pre- 
cisionlhan  the  subdivision  of  the  arm  of  a  steelyard. 

131.  The  spring  steelyard  is  a  very  convenient  instru- 
ment for  weighing  in  cases  where  the  subdivisions  of  weights 
are  large.     It  depends  on  the  elasticity  of  a  spiral  steel 
spring,  to  compress  or  extend  which  requires  a  force  pro- 
portioned to  the  degree  of  compression  or  extension.     The 
manner  of  applying  it  will  be  easily  understood  from  the 
representation  in  figure  28.     After  continued  use,   espe- 
cially when  loaded  with  heavy  weights,  the  elasticity  of 
the  spring  is  liable  to  be  impaired,  and  the  accuracy  of  the 
instrument  diminished.     When  made,  however,  in  the  best 
manner,  spring  steelyards  retain  their  accuracy  for  a  long 
time. 

132.  The  steelyards  or  balance  used  for  estimating  very  heavy 
weighty  as  loaded  carts,  depends  upon  the  principle  of  the  com- 
pound lever.     The  several  levers  are  usually  placed  beneath  a  plat- 
form, which  rests  on  pivots  connected  with  the  shorter  arms,  while 
the  counterpoise  is  connected  with  the  extremity  of  the  longer  arms. 


MACHINERY.  65 

In  figure  29,  is  repre-  FiS-  29 

sented  a  weighing  ma- 
chine employed  in  Eng- 
land, for  estimating  loads 
that  are  transported  on 
turnpike  roads.  It  con- 
sists of  a  platform  rest- 
ing on  four  levers  of  the 
second  kind,  the  weight 
being  between  the  ful-  C 
crum  and  the  power.  The  fulcrums  are  A,  B,  C,  D,  and  the  plat- 
form, and  consequently  the  weight  rests  on  the  points  a,  b,  c,  d. 
Suppose  AF  to  be  ten  times  the  length  of  Aa,  then  10  pounds  at  F, 
would  balance  100  pounds  at  «,  and  if  the  arm  EG  is  ten  times  the 
length  of  EF,  then  ten  pounds  at  G  will  balance  100  pounds  at  F. 
Let  us  then  apply  10  Ibs.  at  G;  this  pressing  upon  F  with  the  force 
of  100  Ibs.,  will  press  upon  a  with  the  force  of  1000  pounds.  This 
would  be  the  case  were  only  one  lever  employed  in  the  place  of  the 
four :  the  fulcrums  a,  b,  c,  dj  divide  this  pressure  equally  among 
themselves. 

133.  When  a  weight  is  supported  by  a  lever  which  rests  on  two 
props  the  pressure  upon  both  fulcrums  is  equal  to  the  whole  weight. 
This  principle  is  sometimes  applied  in  ascertaining  the  weight  of  a 
body  too  heavy  for  the  steelyards.     The  body  is  suspended  immov- 
ably near  the  center  of  a  pole,  and  the  steelyards  are  applied  to  each 
end  of  the  pole  separately,   the  other  end  meanwhile  resting  on  its 
fulcrum.     The  two  weights  being  added  together,  make  the  entire 
weight  of  the  body.     If  the  body  is  suspended  exactly  in  the  center 
of  the  pole,  it  will  be  sufficient  to  obtain  the  weight  of  one  end  and 
double  it.     The  weight  of  the  lever  should,  in  both  cases,  be  sub- 
tracted from  the  entire  weight. 

134.  Since  when  a  weight 'is  sustained  between  two  props,  the 
part  sustained  by  each  prop  is  inversely  as  the  distance  of  the  weight 
from  it,  it  follows  that  a  load  borne  on  a  pole,  between  two  bearers, 

is  distributed  in  this  ratio.     As  the  effort  of  the  bearers,  and  the  di- 
rection of  the  weight  are  always  parallel,  it  makes  no  difference 

9 


66  MECHANICS. 

whether  the  pole  is  parallel  to  the  horizon  or  inclined  to  it.  Wheth- 
er the  bearers  ascend  or  descend,  or  move  on  a  level  plane,  the 
weight  will  be  shared  between  them  in  the  same  constant  ratio. 

135.  Handspikes  and  croivbars  are  familiar  examples  of  levers  of 
the  first  kind.     A  hammer  affords  an  example  of  the  bent  lever; 
and  shears,   pliers,    nutcrackers,   and   all  similar  instruments,    are 
double  levers;  that  is,  they  consits  of  two  levers  united.     A  pair  of 
shears  with  long  handles,  like  those  used  by  tinners,   exhibit  very 
strikingly  the  increase  of  power  gained  by  bringing  the  weight  or 
substance  acted  on  riearer  to  the  fulcrum.     The  jaws  of  animals  ex- 
hibit a  similar  property.     An  oar,  applied  to  a  boat  rowed  by  hand, 
a  wheelbarrow,  and  a  door  shut  by  the  hand  applied  to  the  edge  re- 
mote from  the  hinges,  severally  furnish  instances  of  levers  of  the  se- 
ond  kind,  where  the  weight  is  between  the  fulcrum  and  the  power. 

136.  The  erane  is  a  lever  of  the  second  kind  which  is  much  used 
when  great  weights  are  transported  for  a  short  distance,   as  heavy 
boxes  of  merchandize  from  a  vessel  to  the  wharf,  or  great  masses  of 
stone  from  the  quarry  to  a  car  or  boat.     An  example  of  the  crane, 
on  a  small  scale,  is  seen  in  the  apparatus  of  a  kitchen  fire-place. 

137.  When  one  raises  a  ladder  from  the  ground  by  one  of  the 
lower  rounds,  the  ladder  becomes  a  lever  of  the  third  kind,  the  pow- 
er being  applied  between  the  weight  and  the  prop.     Since  in  all 
the  mechanical  powers,  the  power  and  weight  have  equal  momenta, 
and  since,  in  the   third  kind  of  lever,  the  weight  has  more  velocity 
than  the  power,  the  power  is  as  much  greater  than  the  weight,  as  the 
velocity  with  which  it  moves  is  less.     The  difficulty  experienced  in 
raising  a  ladder  from  the  ground  by  taking  hold  of  the  lowest  round, 
or  of  shutting  a  door  by  applying  the  hand  to  the  side  next  to  the 
hinges,  shews  the   mechanical  disadvantage  under  which  a  lever  of 
this  kind  acts.     Yet  it  is  very  useful  in  cases  where  it  is  required  to 
give  great  velocity  to  the  body  moved.     Sheep  shears,  consist  of  two 
levers  of  this  kind  united.     Here  the  whole  force  required   is  so 
small  that  to  save  it  is  of  no  consequence,  while  so  soft  and  flexible 
a  substance  .as  wool,  requires  the  shears  to  be  moved  with  consider- 
able velocity.     A  pair  of  tongs  is  composed  in  the  same  manner ; 
and  therefore  it  is  only  a  small  weight  that  we  can  lift  with  them,  es- 
pecially when  the  legs  are  long. 


MACHINERY.  67 

138.  One  of  the  most  remarkable  applications  of  the  third  kind 
of  lever,  is  in  the  bones  of  animals.  These  are  levers,  the  joints  are 
the  fulcrums,  and  the  muscles  are  the  power.  The  muscles  are 
endowed  with  a  strong  power  of  contraction,  by  which  they  are  made 
to  pull  upon  a  tendon  or  cord,  which  is  inserted  in  the  bone  near  the 
fulcrum.  Thus,  the  fore-arm  moves  on  the  joint  near  the  elbow 
as  a  fulcrum,  a  little  below  which  is  inserted  a  tendon,  connected 
with  a  muscle  near  the  shoulder  called  the  deltoid  muscle.  The 
arrangement  may  be  well  represented  by  attaching  a  small  cord  to 
one  of  the  legs  of  a  pair  of  tongs,  near  the  joint.  It  will  require 
a  considerable  force  to  lift  the  leg  by  pulling  at  the  string,  especially 
if  the  string  be  pulled  in  a  direction  nearly  parallel  with  the  leg,  as 
it  ought  to  be,  since  the  tendon  which  lifts  the  fore-arm  acts  in  such 
a  direction  with  respect  to  the  arm.  The  muscles  therefore  act,  in 
moving  thfft)ones,  under  a  double  mechanical  disadvantage,  their 
force  being  applied  both  obliquely  and  very  near  the  fulcrum.  The 
force  which  the  deltoid  muscles  exert  in  raising  a  weight  held  in  the 
palrn  of  the  hand,  is  enormous,  as  will  be  comprehended  from  the 
following  illustration.  Let  AB  represent  the  fore-arm,  moving  on  the 
D  Fig.  so. 


elbow-joint  at  A.  and  having  the  tendon  inserted  at  C,  which  we  will 
suppose  to  be  one  hundred  times  nearer  to  A  than  B  is  to  A.  *  Con- 
sequently, a  weight  of  1  Ib.  at  B,  would  require  a  force  at  C,  acting 
directly  upwards,  of  100  Ibs.  But  the  force  of  the  tendon  does  not 
act  directly  upwards  in  the  direction  of  CD,  but  very  obliquely,  as  in 
the  direction  of  CE,  of  which  the  part  E  A  only  can  contribute  to  sup- 
port the  weight.  Suppose  this  part  to  equal  y^th  of  the  whole  force 
CE,  and  it  follows  that  the  muscular  force  exerted  to  raise  a  weight 
of  1  Ib.  in  the  palm  of  the  hand,  would,  were  it  to  act  without  any 
mechanical  disadvantage,  be  sufficient  to  raise  a  weight  of  1000  Ibs. 
Yet  Dr.  Young  informs  us,  that  a  few  years  ago  there  was  a  person 
at  Oxford,  who  could  hold  his  arm  extended  for  half  a  minute,  with 
half  a  hundred  weight  hanging  to  his  little  finger. 

139.  But  by  giving  to  the  muscle  the  position  it  has,  the  greatest 
possible  compactness  of  structure  is  obtained,  while  by  making  it  act 


Oo  MECHANICS. 

« 

so  near  the  fulcrum,  wHat  is  lost  in  force,  is  gained  in  velocity ;  and 
while  the  power  acts  through  a  small  space,  the  hands  are  moved 
quickly  through  a  great  distance.  In  consequence  of  the  dominion 
which  man  can  gain  over  the  stronger  animals,  and  especially  over 
the  great  powers  of  Nature,  he  has  little  occasion  to  exert  great 
strength  with  his  naked  hands :  the  celerity  of  their  movements,  is 
to  him  a  far  more  important  endowment. 


CHAPTER  IX. 

MACHINERY  CONTINUED.— OF  WHEEL  WORK. 

140.  When  a  lever  is  applied  to  raise  a  weight,  or  to  overcome 
a  resistance,  the  space  through  which  it  acts  at  one  time  is  small,  and 
the  work  must  be  accomplished  by  a  succession  of  short  and  inter- 
mitting efforts.  The  common  lever  is,  therefore,  used  only  in  cases 
where  weights  are  required  to  be  raised  through  small  spaces.  When 
a  continuous  motion  is  to  be  produced,  as  in  raising  ore  from  a  mine, 
or  in  weighing  the  anchor  of  a  vessel,  some  contrivance  must  be  adopt- 
ed to  remove  the  intermitting  action  of  the  lever,  and  render  it  con- 
tinual. The  wheel  and  axle,  in  its  various  forms,  fully  answers  this 
purpose.  It  may  be  considered  as  a  revolving  lever. 

Thus  in  Fig.  31,  DE,  is  an  axle  resting  upon  two  supports,  Land 

Fig.  31. 

N  T 

~  S 


JVI 


IT 


MACHINERY.  69 

M ;  NAO,  SVU  are  wheels  connected  with  the  axle ;  W  is  the 
weight  which  may  be  balanced  either  by  a  weight,  hung  to  the  cir- 
cumference of  the  wheel  as  w,  or  by  a  power  applied  in  the  manner 
of  P.  The  latter  mode  renders  obvious  the  analogy  between  the 
lever  and  the  wheel  and  axle,  since  PK,  one  of  the  spokes  of  the 
wheel,  evidently  corresponds  to  a  lever  of  the  first  kind. 

In  the  wheel  and  axle,  the  law  of  equilibrium  is  as  follows  : 
The  power  is  to  the  weight  as  the  diameter  of  the  axle  is  to  the  diam- 
eter of  the  wheel. 

If  the  diameter  of  the  wheel  is  ten  times  that  of  the  axle,  a  power 
of  one  pound  will  balance  a  weight  of  ten. 

141.  In  numerous  forms  of  the  wheel  and  axle,  the  weight  is  ap- 
plied by  a  rope  coiled  upon  the   axle ;  but  the  manner  in  which  the 
power  is  applied  is  very  various,-  and  not  often  by  means  of  a  rope. 
The  circumference  of  a  wheel  sometimes  carries  projecting  pins,  to 
which  the  hand  is  applied  to  turn  the  machine,  as  in  Fig.  31.     An 
instance  of  this  occurs  in  the  wheel  used  in  the  steerage  of  a  vessel. 
In  the  common  windlass  the  power  is  ap- 
plied by  means  of  a  winch  which  corres- 
ponds to   the  radius  of  a  wheel.     The 

axis  is  sometimes  placed  in  a  vertical  po- 
sition, and  turned  by  levers  moved  hori- 
zontally. The  capstan  of  a  ship  (Fig. 
32.)  is  an  example  of  this.  Levers  an- 
swering to  the  radii  of  a  wheel  are  inser- 
ted in  holes  mortised  in  the  axis,  and  turned  by  several  men  work- 
ing together.  In  some  cases,  as  in  the  treadmill,  the  wheel  is  turn- 
ed by  the  weight  of  animals  walking  on  the  circumference  with  a 
motion  like  that  of  ascending  a  steep  hill. 

142.  In  the  COMPOUND  WHEEL  AND  AXLE,  the  power  is  to  the 
weight  as  the  product  of  the  diameters  of  all  the  smaller  wheels  is  to 
the  product  of  the  diameters  of  all  the  larger  ivheels. 


70 


MECHANICS. 


Thus  in  Fig.  33,  the  pow-  Fig.  33, 

er  being  applied  to  the  winch 
PQ  acts  upon  the  small  wheel 
A,  which  acts  upon  the  large 
wheel  B,  this  upon  C,  and  so 
on.  Now  if  the  diameters  of 
the  three  smaller  wheels  in- 
cluding that  of  the  axle,  be 
severally  one  fourth  those  of 
the  larger  wheels,  (of  which 
the  diameter  of  the  wheel  de- 
scribed by  the  winch  PQ,  that 
is,  twice  PQ,  must  be  consid- 
ered as  one)  then  the  pow- 
er will  be  to  the  weight  as  IXlXl  :  4x4x4,  that  is,  as  1  to  64 ; 
and  a  force  of  ten  pounds  applied  at  P  will  balance  a  weight  of  640 
pounds  applied  at  W. 

143.  It  is  sometimes  desirable  to  make  a  variable  power  produce 
a  constant  force.  This  may  be  done  by  making  its  velocity  increase 
as  its  intensity  diminishes.  We  have  an  example  of  this  in  the  re- 
ciprocal action  between  the  main  spring  and  fusee  of  a  watch.  (Fig. 
34.)  The  main  spring  is  coiled  up  in 
the  box  A,  and  is  connected  with  the 
fusee  B  by  a  chain.  When  the  watch 
is  first  wound  up,  the  spring  acts  with 
its  greatest  intensity,  but  then  as  the 
wheel  B  turns,  it  uncoils  with  the 

least  velocity  ;  but  on  account  of  the  varying  diameters  of  the  wheels 
of  the  fusee,  the  velocity  is  continally  increased  as  the  intensity  of 
the  spring  is  diminished.  In  a  similar  manner  a  varying  weight  may 
be  moved  by  a  constant  power. 

144.  Examples. 

Ex>l.  The  diameter  of  a  wheel  is  4j  feet,  and  that  of  its  axis  1| 
:  what  power  will  be  required  to  balance  a  weight  of  100  Ibs.  ? 

4J  :  ij : :  100  :  yj  =2  Ibs.  123-  oz.  Ans. 


Fig.  34. 


MACHINERY.  71 

Ex.  2.  What  must  be  the  diameter  of  a  wheel  by  which  a  weight 
of  100  Ibs.  suspended  by  a  rope  going  round  an  axle  whose  diameter 
is  1  foot,  is  balanced  by  a  power  of  12  Ibs.? 

12 Ibs. :  100  Ibs.  ::i  :  "Ty=8ifeet,  Ans- 

Ex.  3.  A  power  of  3  Ibs.  acts  upon  a  wheel  whose  diameter  is  6 
feet;  what  weight  will  balance  it  upon  an  axle  of  5  inches  diameter? 
Ans.  431  Ibs. 

Ex.  4.  A  power  of  5  Ibs.  balances  a  weight  of  150  Ibs.  by  means  of 
a  wheel  10  feet  in  diameter  :  what  is  the  diameter  of  the  axle?  Ans. 
4  inches. 

Ex.  5.  Four  wheels,  A,  B,  C,  D,  whose  diameters  are  5,  4,  3,  2 
feet  respectively,  are  put  in  motion  by  a  power  of  10  Ibs.  applied  at 
the  circumference  of  the  wheel  A  ;  the  wheels  act  upon  each  other 
by  means,  of  three  smaller  wheels,  the  diameter  of  each  of  which  is 
8  inches ;  the  last  wheel  D,  turns  an  axle  whose  diameter  is  6  in- 
ches ;  what  weight  may  be  sustained  by  a  rope  going  over  the  axle  ? 
Ans.  8100  Ibs. 

Communication  of  Motion  by  Wheel  Work. 

145.  Motion  may  be  transmitted  by  means  of  wheel  work  in  seve- 
ral different  methods,  the  principal  of  which  are,  the  friction  of  the 
circumference  of  one  wheel,  upon  that  of  another — the  friction  of  a 
band — and  the  action  of  teeth. 

One  wheel  is  sometimes  made  to  turn  another,  by  the  mere  fric- 
tion of  the  two  circumferences.  If  the  surfaces  of  both  were  per- 
fectly smooth  so  that  all  friction  were  removed,  it  is  obvious  that 
either  would  slide  over  the  surface  of  the  other,  without  communica- 
ting motion  to  it.  But,  on  the  other  hand,  if  there  were  any  asper- 
ities, however  small  upon  their  surfaces,  they  would  become  mutu- 
ally inserted  among  each  other,  and  neither  the  wheel  nor  axle 
could  move  without  causing  the  asperities  on  its  edge  to  encounter 
those  which  project  from  the  surface  of  the  other ;  and  thus  both 
wheel  and  axle  would  move  at  the  same  time.  Hence  if  the  surfa- 
ces of  the  wheel  and  axle  are  by  any  means  made  rough,  and  press- 
ed together  with  sufficient  force,  the  motion  of  either  will  turn  the 
other,  provided  the  load  or  resistance  be  not  greater  than  the  force 
necessary  to  break  off  these  small  projections  which  produce  friction. 


72  MECHANICS. 

146.  In  some  cases  where  great  power  is  not  required,  motion  is 
communicated  in  this  way  through  a  train  of  wheel  work,  by  render- 
ing the  surfaces  of  the  wheel  and  axle  rough,  either  by  facing  them 
with  buff  leather,  or  with  wood  cut  across  the  grain.  The  commu- 
nication of  motion  between  wheels  and  axles  by  friction  has  the  ad- 
vantage of  great  smoothness  and  evenness,  and  of  proceeding  with 
little  noise ;  but  this  method  can  be  used  only  in  cases  where  the 
resistance  is  not  very  considerable,  and  therefore  it  is  seldom  adopted 
in  works  on  a  large  scale.  Dr.  Gregory  mentions  an  instance  of  a 
saw  mill  at  Southampton,  where  the  wheels  act  upon  each  other,  by 
the  contact  of  the  end  grain  of  the  wood.  The  machinery  makes 
very  little  noise  and  wears  well,  having  been  used  not  less  than 
twenty  years. 

147.  Wheel  work  is  extensively  moved  by  the  friction  of  aband. 
When  a  round  cord  is  used,  any  degree  of  friction  may  be  produced, 
by  letting  the  cord  run  in  a  sharp  groove  at  the  edge  of  the  wheel. 
When  a  strap  or  flat  band  is  used,  its  friction  may  be  increased  by 
increasing  its  width.  The  surface  at  the  circumference  of  a  wheel 
which  carries  a  flat  band,  should  not  be  exactly  cylindrical,  but  a 
little  convex,  in  which  case  if  the  band  inclines  to  slip  off  at  either 
side,  it  returns  again  by  the  tightening  of  its  inner  edge,  as  may  be 
seen  in  a  turner's  lathe.  When  wheels  are  connected  in  the  shortest 
manner  by  a  band,  they  move  in  the  same  direction  ;  if  the  band  be 
crossed,  they  will  move  in  opposite 
directions.  (Fig.  35.)  Wheels 
are  sometimes  turned  by  chains  in- 
stead of  straps  or-  bands,  and  are 
then  called  rag  wheels.  The 
chains  lay  hold  upon  pins,  or  en- 
ter into  notches,  in  the  circumfe- 
rence of  the  wheels  so  as  to  cause 

Tl 

them  to  turn  simultaneously.  They 

are  used  when  it  is  necessary  that 

the  velocities  should  be  uniform, 

and  where  great  resistance  is  to  be  overcome,  as  in  locomotive  steam 

engines,  chain  water  wheels;  &c. 


MACHINERY. 


Fig.  36. 


148.  But  the  most  common  mode  of  moving  wheel  work,  is  by 
means  of  teeth  cut  in  the  circumference  of  the  wheels.     The  wheels 
of  necessity  turn  in  opposite  directions.     The  connexion  of  one 
toothed  wheel  with  another  is  called  gearing.     In  the  formation  of 
teeth,  very  minute  attention  must  be  given  to  their  figure,  in  order 
that  motion  may  be  communicated  from  one  wheel  to  another,  with- 
out rubbing  or  jarring.     If  the  teeth  are  ill  matched  as  in  figure  36, 
when  the  tooth  A,  comes  into  contact  with  JB, 

it  acts  obliquely  upon  it,  and  as  it  moves,  the 
corner  of  B  slides  upon  the  plane  surface  of 
A  in  such  a  manner  as  to  produce  much  fric- 
tion, and  to  grind  away  the  side  of  A,  and  the 
end  of  B.     As  they  approach  the  position  CD, 
they  sustain  a  jolt  the  moment  their  surfaces 
come  into  full  contact ;  and  after  passing  the 
position  CD,  the  same  scraping  and  grinding 
effect  is  produced  in  the  opposite  direction,  until  by  the  revolution  of 
the  wheels  the  teeth  become  disengaged.     To  avoid  these  evils,  the 
surfaces  of  the  teeth  are  frequently  curved  so  as  to  roll  on  each  other 
with  as  little  friction,  and  with  as  uniform  force  and  velocity  as  pos- 
sible. (Fig.  37.)     Much  pains  and  skill  have 
been  bestowed  on  this  subject  by  mathemati- 
cians, with  the  view  of  ascertaining  the  kinds 
of  curves  which  fulfil  these  purposes  best. 

Regulation  of  Velocity  by  Wheel  Work. 

149.  Wheel  work  serves  the  purpose,  not 
only  of  forming  a  convenient  communication  of 
motion  between  the  power  and  the  weight,  but 
also  of  regulating  its  velocity.-  Thus,  when  the 

connexion  is  formed  by  means  of  a  band,  as  in  figure  35,  the  veloci- 
ty of  the  wheel  B,  that  carries  the  weight  or  sustains  the  pressure  may 
be  altered  at  pleasure,  by  altering  the  ratio  between  the  diameters' of 
the  two  wheels.  If  the  diameters  are  equal,  the  wheels  will  revolve 
with  equal  velocity;  if  A  remains  the  same,  while  the  diameter  of  B 
is  increased  or  diminished,  the  velocity  of  B  will  be  increased  or  di- 
minished in  the  same  ratio;  or  if  B  remains  the  same,  while  the  di- 
ameter of  A  is  changed,  the  velocity  of  B  will  be  changed  in  the 

10 


74  MECHANICS. 

same  manner.  We  see  familiar  examples  of  the  application  of  this 
principle  in  the  common  spinning  wheel,  and  the  turner's  lathe.  In 
the  spinning  wheel,  a  band  passes  round  a  large  wheel  and  a  small 
one  called  a  spool,  having  the  spindle  for  its  axis;  and  in  consequence 
of  the  great  disparity  in  the  size  of  the  wheels,  a  grefit  velocity  is 
given  to  the  spindle  by  a  comparatively  slow  revolution  of  the  wheel. 
In  a  turner's  apparatus,  machinery  for  spinning  cotton,  and  the  like, 
a  large  hollow  cylinder  or  drum,  is  fixed  horizontally,  which  is  kept 
revolving  by  the  moving  power,  and  from  which,  motion  is  convey- 
ed by  bands  to  lathes,  spindles,  &ic.,  to  which  any  required  veloci- 
ty is  given,  by  altering  the  diameter  of  the  small  wheel  that  is  con- 
nected with  them  and  turns  them.  Sometimes  a  change  of  veloci- 
ty is  effected  by  making  the  drum  of  a  conical  shape,  and  then  the 
velocity  imparted  to  the  lathe  or  the  spindle,  will  be  greater  or  less, 
according  as  the  band  proceeds  from  the  larger  or  smaller  part  of 
the  drum. 

150.  A  more  exact  method  of  regulating  the  velocity  of  motion, 
is  by  means  of  wheels  and  pinions.     An   example  of  this  kind  is 
seen  in  Fig.  38.  where  A,  B,  C,  are  three  wheels,  and  #,  &,  c,  are 
the  corresponding  pinions.     As 

the  leaves  of  the  pinions  succes- 
sively pass  between  the  teeth  of 
the  wheel,  they  must  be  equal 
and  similar  to  them ;  and  since 
magnitudes  have  the  same  ratio 
to  each  other  as  their  like  parts, 
it  follows  that  the  number  of 
teeth  in  a  wheel,  and  of  leaves 
in  the  pinion  that  acts  upon  it, 
express  the  ratio  of  the  circum- 
ference or  radius  of  the  wheel  to  that  of  the  pinion.  Hence,  in  an 
equilibrium,  the  power  multiplied  by  the  product  of  the  numbers  ex- 
pressing the  amount  of  teeth  in  all  the  wheels  respectively,  is  equal 
to  the  ^eight  multiplied  by  the  product  of  the  several  numbers  deno- 
ting the  leaves  in  each  of  the  pinions. 

151.  It  is  farther  evident  that  the  velocity  of  a  wheel  and  that  of 
the  pinion  connected  with  its  circumference,  will  be  inversely  as  the 


MACHINERY. 


75 


number  of  teeth  in  each.  Thus  in  Fig.  38.  if  the  pinion  a  has  10 
teeth,  and  the  wheel  B  has  100,  a  will  move  ten  times  as  fast  as  B. 
For  the  same  reason  b  will  move  ten  times  as  fast  as  C,  so  that,  in 
this  arrangement,  the  power  moves  with  100  times  the  velocity  of  the 
weight.  By  varying  the  ratio  between  the  number  of  teeth  in  the 
pinion,  arid  the  number  of  teeth  in  the  wheel  with  which  it  is  con- 
nected, we  may  vary  the  velocity  of  any  wheel  at  pleasure. 

152.  A  familiar  instance  of  this  is  afforded  in  the  mechanism  of 
a  common  clock.     A  pendulum  by  falling  gains  a   quantity  of  mo- 
tion sufficient  to  carry  it  on  the  other  side  to  the  same  height  as  that 
from  which  it  fell ;  and  were  it  not  for  the  resistance  of  the  air  and 
the  impediments,  a  pendulum  when  once  set  in  motion  would  con- 
tinue to  vibrate  by  its  own  inertia,   and  would  thus  afford,  without 
the  aid  of  any  machinery,  an  exact  measure  of  time.     But,  in  order 
to  continue  its  vibrations,  some  small  force  must  be  applied  to  it  to 
compensate  for  the  loss  of  motion  from  friction  and  resistance.     This 
force  is  supplied   to  the  pendulums  of  clocks  by  the  weight,  and  an 
analogous  force  is  supplied  to  the  balance  wheel  of  watches  and 
chronometers  by  springs.     In  Fig.  39.  let  A  B 

be  a  wheel  having  30  teeth,  and  let  N,  M,  be  a 
pendulum,  connected  with  the  wheel  by  the 
pallets  I,  K ;  and  to  the  axis  a,  let  a  weight 
be  hung.  It  is  evident  that  this  weight,  were 
there  nothing  to  arrest'  it,  would  descend  by 
the  force  of  gravity  with  accelerated  velocity. 
It  endeavors  thus  to  descend,  and  hence  exerts 
the  required  force  on  the  pallets  of  the  pendu- 
lum. For,  every  time  the  pendulum  performs 
a  double  vibration*,  (returning  to  the  same 
point  from  which  it  set  out)  a  tooth  of  the 
wheel  escapes,*  and  the  wheel  runs  down  until 
the  next  tooth  strikes  upon  the  pallet,  and  thus 
gives  it  the  impulse  which  is  necessary  to  keep 
up  the  vibrations. 

153.  It  would  seem  therefore  that,  for  beating  seconds,  only  a  sin- 
gle wheel  is  necessary ;  nor  would  any  more  be  absolutely  indispen- 


Fig.  39. 


K 


*  Hence  this  wheel  is  called  the  scapement. 


76  MECHANICS. 

sable ;  but  in  this  case  the  weight  would  descend  so  fast,  as  soon  to 
reach  the  floor,  and  the  clock  would  require  to  be  wound  up  again 
every  few  minutes.  Hence  a  series  of  wheels  are  interposed  be- 
tween the  pendulum  and  the  weight,  by  which  the  descent  of  the 
latter  is  retarded  upon  the  principle  explained  in  Art.  151.  and  the 
descent  of  the  weight  is  slower  in  proportion  as  the  series  is  more 
extensive.  In  cheap  clocks,  as  some  of  those  made  with  wooden 
wheels,  the  series  is  short,  or  the  number  of  wheels  employed  for  re- 
tarding the  descent  of  the  weight  is  small,  and  such  clocks  require 
frequent  winding  up ;  but  in  clocks  of  finer  workmanship,  a  greater 
number  of  wheels  is  interposed,  and  such  clocks  require  to  be  wound 
up  less  frequently.  Many  go  eight  days,  and  some  are  made  to  go  a 
whole  year  without  winding. 

Wheel  Carriages. 

154.  In  wheel  carriages,  wheels  are  not  used  as  mechanical  pow- 
ers ;  for,  since  they  move  with  the  same  velocity  as  the  power  which 
propels  them,  there  is  no  mechanical  advantage  gained  by  them. 
When  we  shut  a  door  by  taking  hold  of  the  edge  most  remote  from 
the  hinges,  the  door  becomes  a  lever  of  the  second  kind,  and  we 
act  under  a  mechanical  advantage.  When  we  shut  the  door  by  ap- 
plying the  hand  near  the  hinge,  the  door  becomes  a  lever  of  the 
third  kind,  and  we  act  under  a  mechanical  disadvantage.  There  is, 
however,  a  point  between  the  inner  and  outer  edge,  where  the  force 
would  act  without  either  advantage  or  disadvantage.  In  like  man- 
ner, a  carriage  wheel  is  turned  on  the  ground  as.on  a  hinge  by  a 
force  applied  at  its  center  of  gravity  ;  and,  in  passing  over  an  obsta- 
cle, it  rolls  over  it  as  a  door  turns  on  its  hinges.  The  necessity  of 
a  certain  amount  of  resistance  or  friction  in  the  plane  on  which  the 
wheel  revolves  is  obvious,  because  otherwise  there  could  be  no  ful- 
crum or  hinge  on  which  it  could  turn.  Thus  wheels  moving  on 
smooth  ice,  slide  instead  of  turning ;  and  when  the  power  is  applied 
to  the  circumference,  if  the  friction  is  not  sufficient  to  act  as  a  ful- 
crum, the  wheel  turns  without  advancing,  as  a  wheel  turning  in  the 
air.  Large  wheels  appear  in  theory  to  be  much  more  advantageous 
than  small  ones.  A  large  wheel  will  better  surmount  stones  and 
other  obstacles,  since  in  turning  over,  the  ascent  is  more  gradual  and 
easy.  In  passing  over  holes,  it  sinks  less,  and  occasions  less  jolting 
and  less  expenditure  of  power.  The  wear  of  small  wheels  exceeds 


MACHINERY.  77 

that  of  large  ones ;  for  if  we  suppose  a  wheel  to  be  three  feet  in  di- 
ameter, it  will  turn  round  twice,  while  a  wheel  of  six  feet  in  diame- 
ter turns  ronnd  once.  Of  course  its  tire  will  come  twice  as  often 
in  contact  with  the  ground,  and  its  spokes  will  twice  as  often  have 
to  support  the  weight  of  the  load.  So  that  by  calculation,  it  should 
last  but  half  the  length  of  time.  On  these  accounts  it  would  be 
advantageous  to  augment  the  diameter  of  wheels  to  a  great  extent 
were  it  not  for  certain  practical  limits  which  it  is  found  useful  not  to 
exceed.  One  of  them  is  found  in  the  nature  of  the  materials  which 
we  are  obliged  to  use,  and  which  if  employed  to  make  wheels  of 
great  size  at  the  same  time  preserving  the  requisite  strength,  would 
render  them  cumbersome  and  too  heavy  for  use.  Again,  a  wheel 
should  seldom  be  of  such  dimensions,  that  its  center  is  higher  than 
the  breast  of  the  horse  or  other  animal  by  which  it  is  drawn ;  because 
when  this  is  the  case,  the  horse  draws  obliquely  downwards  as  well 
as  forward,  and  expends  a  part  of  his  strength  against  the  ground. 

155.  The  line  of  draught  should  not  be  horizontal  but  inclined 
upwards  towards  the  breast  of  the  horse,  in  an  angle  not  less  than 
15  degrees  with  the  horizon.     This  brings  the  strain  nearly  at  right 
angles  with  the  collar,  whereas  a  horizontal  draught  lifts  the  collar 
upwards,  by  which  the  force  is  wasted  and  the  animal  is  choked. 

156.  The  effect  of  suspending  a  carriage  on  springs,  is  to  equal- 
ize the  motion  by  causing  every  change  to  be  more  gradually  com- 
municated to  it,  and  to  obviate  shocks.     Springs  are  not  only  useful 
for  the  convenience  of  passengers,  but  they  also  diminish  the  labor 
of  draught ;  for  whenever  a  wheel  strikes  a  stone,  it  rises  against  the 
pressure  of  the  spring,  in  many  cases  without  materially  disturbing 
the  load,  whereas  without  the  spring,  the  load,  or  a  part  of  it,  must 
rise  with  every  jolt  of  the  wheel,  and  will  resist  the  change  of  place 
with  a  degree  of  inertia  proportionate  to  the  weight,  and  the  sudden- 
ness of  the  percussion.     Hence  springs  are  highly  useful  in  baggage 
wagons  and  other  vehicles  used  for  heavy  transportation. 

A  pair  of  horses  draw  more  advantageously  abreast  than  when  one 
is  harnessed  before  the  other.  In  the  latter  case,  the  forward  horse, 
being  attached  to  the  ends  of  the  shafts,  draws  in  a  line  nearly  hori- 
zontal ;  consequently  he  does  not  act  with  his  whole  force  upon  the 
load,  and  moreover  expends  a  part  of  his  force  in  a  vertical  pressure 
on  the  back  of  the  other  horse. 


78 


MECHANICS, 


CHAPTER  X. 

i     MACHINERY  CONTINUED.— THE  PULLEY,   INCLINED   PLANE, 
SCREW  AND  WEDGE. 

THE    PULLEY. 

1 57.  A  PULLEY  is  a  small  grooved  wheel  movable  about  a  pivot,  the 
pivot  itself  being  at  the  same  time  either  fixed  or  movable. 

The  fixed  pulley  is  represented  in  Fig.  40. 
By  it  no  mechanical  advantage  is  gained,  but 
its  use  consists  in  furnishing  a  convenient  mode 
of  changing  the  direction  of  the  power.  Thus, 
it  is  far  more  convenient  to  raise  a  bucket  from 
a  well  by  drawing  downwards,  as  is  the  case 
where  the  rope  passes  over  a  fixed  pulley  above 
the  head,  than  by  drawing  upwards,  leaning 
over  the  well.  By  means  of  the  pulley,  great 
facilities  are  afforded  for  managing  the  rigging 
of  a  ship.  The  sails  at  mast  head  can  be  easily 
raised,  while  the  hands  stand  upon  the  deck, 
whereas,  without  the  aid  of  ropes  and  pulleys, 
the  same  force  removed  to  the  mast  head  would 
operate  under  very  great  disadvantages.  Similar  facilities  are  afforded 
by  this  kind  of  apparatus  for  raising  heavy  weights,  as  boxes  of  mer- 
chandize, or  heavy  blocks  of  stone  in  building. 

Fire  escapes  sometimes  consist  merely 
of  a  pulley  fixed  near  the  window  of  the 
apartment,  around  which  a  rope  may  be 
easily  placed,  having  a  basket  attached  to 
the  end.  The  man  seats  himself  in  the 
basket,  grasping,  at  the  same  moment, 
the  rope  on  the  other  side  of  the  pulley, 
and  thus  he  lets  himself  gradually  down. 

15&»  The  movable  pulley  is  attended 
with  a  mechanical  advantage,  so  that  by 
its  aid,  a  comparatively  small  power  may 
be  made  to  raise  great  weights.  Fig.  41, 
represents  a  movable  pulley  E  in  con- 
nexion with  a  fixed  one  A.  The  weight 


MACHINERY. 


79 


Fig.  42. 


_ 

'-      ..... 


W  bears  equally  upon  the  two  parts  of  the  rope,  and  consequently 
that  which  acts  against  the  power  P  sustains  only  half  the  weight. 
An  equilibrium  will  therefore  be  produced  when  the  power  is  equal 
to  half  the  weight. 

In  Fig.  42,  blocks  of  pulleys  are 
represented,  ,  in  which  the  weight 
is  distributed  over  a  greater  number 
of  parts  of  the  rope ;  each  part  there- 
fore sustains  a  proportionally  smaller 
portion  of  the  load,  and  yet  one  of 
these  parts  is  all  that  acts  immediate- 
ly against  the  power.  Hence  the 
power  will  be  as  much  less  than  the 
weight  as  the  number  of  parts  of  the 
rope  is  greater  than  unity,  Thus, 
where  there  are  six  parts,  three  on 
each  side,  a  power  of  one  pound 
will  balance  a  weight  of  six  pounds. 
This  principle  is  generalized  in  the 
following  proposition. 

In  the  pulley  an  equilibrium  is  pro- 
duced, when  the  power  is  to  the  iveight 
as  one  to  the  number  of  ropes. 

159.  The  ascent  of  the  weight  is  in  all  cases  retarded  in  pro- 
portion as  the  efficacy  of  a  given  power  is  increased.  Moreover,  in 
using  any  system  of  movable  pulleys,  the  whole  weight  of  the  pulleys 
themselves,  together  with  the  resistance  occasioned  by  the  rigidity 
and  friction  of  the  rope,  acts  against  the  power,  and  so  far  lessens 
the  weight  which  it  is  capable  of  raising.  In  the  more  complex  sys- 
tem of  puljeys,  it  is  estimated,  that  at  least  two  thirds  of  the  pow- 
er is  expended  on  the  machinery  itself.  On  account  therefore  of 
slowness  of  the  motion  which  the  weight  receives,  and  the  loss  of 
power  from  the  resistance  of  the  ropes  and  blocks,  such  systems  of 
pulleys  are  seldom  employed.  It  is  only  in  raising  vast  weights, 
such  as  large  ships,  or  great  masses  of  stone  from  a  quarry,  that 
they  are  ever  used.  For  managing  the  rigging  of  a  ship,  the  com- 


80 


MECHANICS. 


bination  usually  employed  consists  of  not  more  than  two  or  three 
movable  pulleys.  From  its  portable  form,  however,  its  cheapness, 
and  the  facility  with  which  it  can  be  applied,  especially  in  changing 
or  modifying  the  direction  of  motion,  the  pulley  is  one  of  the  most 
convenient  and  useful  of  the  mechanical  powers. 

160.  Examples. 

Ex.  1.  I  wish  to  raise  a  block  of  stone  weighing  two  tons,  or  4480 
Ibs.  but  can  command  a  power  only  equal  to  746|  Ibs. :  What  num- 
ber of  pulleys  shall  I  require  ?  746|  ;  4480 : :  1  :  6  ropes,  or  3  mov- 
able pulleys,  Ans. 

Since  the  number  of  ropes  (or  parts  of  the  rope,)  must  be  6,  and 
since  each  movable  pulley  has  two  ropes,  as  in  Fig.  42,  therefore 
the  number  of  movable  pulleys  must  be  three  ;  or  the  block  must  be 
analogous  to  one  of  those  represented  in  Fig.  42. 

In  this  and  other  similar  estimates  no  allowance  is  made  for  the 
weight  of  the  pulleys  and  other  parts  of  the  machinery  which  are 
raised  along  with  the  weight.  The  amount  of  these  must  be  added 
to  the  weight  in  order  to  ascertain  the  power  required. 

Ex.  2.  By  a  system  of  pulleys  containing  6  movable  pulleys,  the 
same  string  going  round  the  whole  as  in  Fig.  42,  what  power  will 
be  necessary  to  sustain  a  weight  of  112  Ibs.  ?  Ans.  9J. 


Fig.  43 


THE  INCLINED  PLANE. 

161.  Let  Fig.  43,  represent  an  Incli- 
ned Plane  whose  length  is  AC,  height 
AB,  and  base  BC ;  and  let  W  be  a  weight 
drawn  up  this  plane  by  a  power  applied 
at  P  and  acting  parallel  to  the  plane. 
Then  an  equilibrium  is  produced,  when 
the  power  is  to  the  weight,  as  the  height 
of  the  plane  to  its  length. 


162,  The  inclined  plane  becomes  a  mechanical  power  in  conse- 
quence of  its  supporting  a  part  of  the  weight,  and  of  course  leaving 
only  a  part  to  be  supported  by  the  power.  •  Thus  the  power  has  to 
encounter  only  a  portion  of  the  force  of  gravity  at  a  time, — a  por- 
tion which  is  greater  or  less,  according  as  the  plane  is  more  or  less 


MACHINERY.  81 

elevated.  When  a  plane  is  perfectly  horizontal,  it  sustains  the  entire 
pressure  of  a  body  that  rests  on  it ;  that  is,  the  pressure  on  the  plane 
is  equal  to  the  whole  force  of  gravity  acting  on  the  body.  As  one 
end  of  the  plane  is  elevated,  this  force  is  resolved  into  two,  one  of 
which  is  parallel  and  the  other  perpendicular  to  the  plane.  In  pro- 
portion as  the  plane  is  more  elevated,  the  part  of  the  force  which  acts 
parallel  with  the  plane  is  increased,  until,  when  the  plane  becomes 
perpendicular  to  the  horizon,  it  no  longer  sustains  any  portion  of  the 
weight,  and  the  latter  descends  with  the  whole  force  of  gravity. 

163.  The  simplest  example  we  have  of  the  application  of  the  In- 
clined Plane,  is  that  of  a  plank  raised  at  the  hinder  end  of  a  cart  for 
the  purpose  of  rolling  in  heavy  articles,  as  barrels  or  hogsheads.  The 
force  required  to  roll  the  body  on  the  plank,  setting  aside  friction, 
is  as  much  less  than  that  required  to  lift  it  perpendicularly,  as  the 
height  of  the  plane  above  the  ground  is  less  than  its  length.  Every 
one  knows  how  much  the  facility  of  moving  heavy  loads  is  increased 
by  such  means,  and  how  the  force  required  to  move  them  is  dimin- 
ished, by  increasing  the  length  of  the  plane  while  the  height  remains 
the  same.  Long  inclined  planes,  constructed  of  plank,  are  frequent- 
ly employed  in  building,  especially  where  high  walls  are  built  of  large 
masses  of  stone,  the  materials  being  trundled  up  the  plane  on  wheel 
barrows,  or  transported  on  heavy  rollers,  ft  is  even  supposed  that 
in  building  the  pyramids  of  Egypt,  the  huge  masses  of- stone  were 
elevated  on  an  inclined  plane.  Roads  also,  except  when  they  are 
perfectly  level,  afford  examples  of  this  mechanical  power.  When  a 
horse  is  drawing  a  heavy  load  on  a  perfectly  horizontal  plane,  what  is 
it  that  occasions  such  an  expenditure  of  force  ?  It  is  not  the  weight 
of  the  load,  except  so  far  as  that  increases  the  friction ;  for  gravity, 
acting  in  a  direction  perpendicular  to  the  horizon,  can  oppose  no  re- 
sistance in  the  direction  in  which  the  load  is  moving.  The  answer 
is,  that  the  force  of  the  horse  is  expended  chiefly  in  overcoming 
friction,  and  the  resistance  of  the  air.  But  when  a  horse  is  drawing 
a  load  up  a  hill,  he  has  not  only  these  impediments  to  encounter,  but 
has  also  to  overcome  more  or  less  of  the  force  of  gravity;  that  is,  he 
lifts  such  a  part  of  the  load  as  bears  to  the  whole  load  the  same  ra- 
tio, that  the  perpendicular  height  of  the  hill  bears  to  its  length.  If 
the  rise  is  one  foot  in  twenty,  he  lifts  on  twentieth  of  the  load,  and 

11 


82  MECHANICS. 

therefore  encounters  so  much  resistance  in  addition  to  the  resistan- 
ces which  he  had  to  overcome  on  the  horizontal  plane.  If  the  ascent 
were  one  foot  in  four,  and  the  load  were  a  ton,  the  additional  force 
required  above  what  would  he  necessary  on  level  ground,  would  be 
560  pounds* 

164.  Railways  afford  another  striking  exemplification  of  the  prin- 
ciples of  the  Inclined  Plane.     By  means  of  them  the  irregular  sur- 
face of  a  country,  however  hilly  and  uneven,  is  reduced  to  horizon- 
tal levels  and  inclined  planes.     These  are  sometimes  inclined  at  so 
low  an  angle,  that  the  tendency  of  the  cars  down  the  plane,  is  only 
just  sufficient  to  balance  their  friction,  and  they  would  remain  at  rest 
of  themselves  in  any  part  of  the  plane,  while  a  small  force  would 
move  them  either  way.     In  other  places  the  Inclined  Planes  are  very 
steep  for  a  short  distance ;  and  the  cars  ascending  upon  them  are 
sometimes  drawn  up  by  means  of  a  power  (a  steam  engine  for  exam- 
ple,) stationed  on  the  summit,  and  sometimes  cars  descending  on  one 
side,  are  made  to  draw  up  others  on  the  other  side,  the  two  being 
connected  by  a  chain  or  rope  which  passes  round  a  pulley  on  the 
summit.     It  is  said  that  on  a  well  constructed  horizontal  railway  a 
single  horse  will  draw  a  load  weighing  ten  tons. 

165.  The  Inclined  Blane  has  been  very  advantageously  substitu- 
ted for  Locks  on  Canals.     The  method,  in  general,  is  to  construct 
around  the  Falls  a  railway  in  the  form  of  an  inclined  plane ;  and 
then  the  boat  being  floated   into  a  large  cistern  of  water,  the  whole 
is  placed  on  the  inclined  plane,   (the  lower  end  of  the  cistern  being 
supported  so  as  to  keep  the  surface  of  the  water  level,)  and  is  rolled 
up  or  down  the  plane,  either  by  making  descending  draw  up  ascend- 
ing loads,  or  by  drawing  up  the  ascending  cistern  with  its  boat  by 
means  of  machinery.     In  the  latter  case,  the  water  fall  itself  acting 
on  a  wheel,  may  be  made  to  afford  the  requisite  power. 

166.  The  motion  of  bodies  descending  down  inclined  planes,  is 
subject* to  the  same  law  of  gravity  as  bodies  falling  freely ;  that  is,  it 
is  uniformly  accelerated.     Consequently,  here,  as  in  the  case  of  bo- 
dies falling  without  impediment,  the  spaces  described  are  proportioned 
to  the  squares  of  the  times,  and  to  the  squares  of  the  velocities  acqui- 
red.    (Arts.  59  and  63.) 


MACHINERY.  83 

167.  The  velocity  acquired  in  fatting  down  an  inclined  plane  is 
the  same  as  that  acquired  in  fatting  through  the  perpendicular  height 
of  the  plane. 

When  a  plane  is  but  slightly  elevated,  as  in  rail-roads,  the  accele- 
ration, though  constant,  is  comparatively  slow;«but  after  rolling  freely 
through  such  a  distance  as  several  miles,  the  motion  may  become 
exceedingly  rapid.  A  very  remarkable  example  of  the  acceleration 
of  bodies  descending  down  inclined  planes,  occurs  at  the  Slide 
of  Alpnach  in  Switzerland.  On  Mount  Pilatus,  near  Lake  Lu- 
zerne,  is  a  valuable  growth  of  fir  trees,  which,  on  account  of  the  in- 
accessible nature  of  the  mountain,  had  remained  for  ages  uninjured, 
until  within  a  few  years,  a  German  engineer  contrived  to  construct  a 
trough  in  the  form  of  an  inclined  plane,  by  which  these  trees  are 
made  to  .descend  by  their  own  weight,  through  a  space  of  eight  or 
nine  miles  from  the  side  of  the  mountain  to  the  margin  of  the  lake. 
Although  the  average  declivity  is  no  more  than  about  one  foot  in  sev- 
enteen, and  the  route  often  circuitous  and  sometimes  horizontal,  yet 
so  great  is  the  acceleration,  that  a  tree  descends  -the  whole  distance 
in  the  short  space  of  six  minutes.  To  a  spectator  standing  by  the 
side  of  the  trough,  at  first  is  heard  on  the  approach  of  a  tree,  a  roar- 
ing noise,  becoming  louder  and  louder ;  the  tree  comes  in  sight  at 
the  distance  of  half  a  mile,  and  in  an  instant  afterwards  shoots  past 
with  the  noise  of  thunder  and  the  rapidity  of  lightning.  WJien  a 
tree  happens  to  "  bolt"  from  the  trough,  it  cuts  the  standing  trees 
quite  off. 

168.  It  takes  as  much  longer  for  a  body  to  descend  down  an  in- 
clined plane,  than  to  fall  through  its  perpendicular  height  as  the 
length  of  the  plane  exceeds  its  height.  A 
Thus,  in  Fig.  44,  a  body  in  .descending 

successively  down  the  planes  AC,  AD, 
AE,  would  acquire  in  each  case  the  same 
velocity,  being  the  same  as  it  would  ac- 
quire by  falling  down  AB ;  but  the  times 


of  describing  these  several  lines  would 
be  proportioned  to  their  respective  lengths. 


84 


MECHANICS. 


THE    SCREW. 

169.  When  a  road,  instead  of  ascending  a  hill  directly,  winds 
round  it  to  the  summit,  so  as  to  lengthen  the  inclined  plane,  and  thus 
aid  the  moving  force,  the  Inclined  Plane  becomes  a  Screw.  In  the 
same  manner  a  flight  of  stairs,  winding  around  the  sides  of  a  cylindri- 
cal tower,  either  within  or  without,  affords  an  instance  of  an  inclined 
plane  so  modified  as  to  become  a  screw.  These  examples  show  the 
strong  analogy  which  subsists  between  these  two  mechanical  powers ; 
or  rather,  they  show  that  the  screw  is  a  mere  modification  of  the 
Inclined  Plane.  This  correspondence  between  the  Inclined  Plane 
and  the  Screw  is  exhibited 
in  the  annexed  figure.  The  FiS-  45- 

distance  between  two  con- 
tiguous threads  of  a  screw, 

corresponds  to  the  height  C 

of  an  inclined  plane,  and 
the  circumference  of  the 
cylinder  corresponds  to  the 
base  of  the  same  plane ; 
hence  the  forces  necessary  to  produce  an  equilibrium  in  the  screw, 
are  the  same  as  in  the  inclined  plane.  Thus,  let  the  inclined  plane 
ABC  be  wrapped  round  a  cylin- 
der, the  circumference  of  whose 
base  is  equal  to  the  line  AB; 
then  the  point  A  being  placed  on 
A7,  the  point  B  will  come  round 
to  A',  and  the  point  C  will  fall  on 
C7,  and  the  line  AC  will  trace 
out  the  thread  of  the  screw  on 
the  surface  of  the  cylinder  as  far 
as  C7,  and  may  be  continued  in 
the  same  manner.  It  will  be  re- 
marked that  the  power  here  acts 
parallel  to  the  base  of  the  incli- 
ned piaffe.  Thus  in  figure  46, 
the  power  is  applied  to  the  han- 
dle B,  which  revolves  parallel  to 
the  base  of  screw,  or  the  base  of 
the  inclined  plane  of  which  the  screw  is  formed 


Fig.  46. 


MACHINERY.  85 

170.  In  the  screw,  an  equilibrium  is  produced  when  the  power  is 
to*the  weight,  as  the  distance  between  two  contiguous  threads  is  to  the 
circumference  of  the  base. 

By  inspecting  figure  45,  it  will  be  seen  that  "the  distance  be- 
tween two  contiguous  threads,"  is  the  height  CB  of  the  inclined 
plane  ABC,  while  "  the  circumference  of  the  base"  is  the  base  AB 
of  the  same  plane.  The  law  of  equilibrium  of  the  screw  is  there- 
fore the  same  as  in  the  inclined  plane  when  the  power  act's  in  a  di- 
rection parallel  with  the  base ;  in  this  case  the  power  being  to  the 
weight  as  the  height  of  the  plane  to  the  base. 

171.  The  power  however  is  not  always  applied  directly  to  the 
circumference  of  the  screw,  but  frequently  at  the  end  of  a  lever  in- 
serted into  the  screw  as  in  figure  46,  and  as  in  the  common  cider  press. 
Hence  a  more  general  law  of  equilibrium  is  as  follows  : 

In  the  screw,  an  equilibrium  is  produced  when  the  power  is  to  the 
weight,  as  the  distance  between  two  contiguous  threads  is  to  the  cir- 
cumference of  the  circle  described  in  one  revolution  of  the  power. 

172.  The  Screw  is  generally  employed  where  severe  pressure  is 
to  be  exerted  through  small  spaces,   and  is  therefore  the  agent  in 
most  presses.     Being  subject  to  great  loss  from  friction,  (upon  which 
however,  its  chief  utility  depends,  as  will  be  shown  hereafter,)  it  usu- 
ally exerts  but  a  small  power  of  itself,  but  derives  its  principle  effi- 
cacy from  the  lever,  or  from  wheelwork,  with  which  it  is  very  easily 
combined.     Thus,  in  figure  46,  were  the  power  applied  directly  to 
the  screw,  the  mechanical  advantage  gained  wpuld  hardly  more  than 
compensate  for  the  loss  by  friction  ;  but  by  means  of  the  lever  (which 
may  be  lengthened  or  shortened  at  pleasure)  the  power  is  greatly  in- 
creased.    The  endless  screw  is  represented  in  figure  48.     It  is  used 
in  connexion  with  toothed  wheels.     By  means  of  the  endless  screw, 
combined  with  the  wheel  and  axle,   a  very  powerful  force  may  be 
exerted ;  and  as  the  mechanical  power  of  the  screw  depends  upon 
the  relative  magnitude  of  the  circumference  through  which  the  pow- 
er revolves,  and  the  distance  between  the  threads,  it  is  evident  that, 
to  increase  the  efficacy  of  the  machine,  we  must  either  increase  the 
length  of  the  lever  by  which  the  power  acts,  or  diminish  the  distance 


86  MECHANICS. 

between  the  threads.  Although,'  in  theory,  there  is  no  limit  to  the 
increase  of  the  mechanical  efficacy  by  these  means,  yet  practical fn- 
convenience  arises  from  the  great  space  over  which  a  very  long  lev- 
er traverses.  If,  on  the  other  hand,  the  power  of  the  machine  is 
increased  by  diminishing  the  distance  between  the  threads,  and  of 
course  their  size,  the  thread  will  become  too  slender  to  bear  a  great 
resistance.  The  cases  in  which  it  is  necessary  to  increase  the  pow- 
er of  the  machine,  being  those  in  which  the  greatest  resistances  are 
to  be  overcome,  the  object  will  evidently  be  defeated,  if  the  means 
chosen  to  increase  that  power,  deprives  the  machine  of  the  strength 
which  is  necessary  to  sustain  the  force  to  which  it  is  to  be  sub- 
mitted. 

173.  These  inconveniences  are  remedied  by  Hunter's  Screiv, 
which,  while  it  gives  to  the  machine .  all  the  requisite  strength  and 
compactness,  allows  it  to  have  an  almost  unlimited  degree  of  me- 
chanical efficacy.  This  screw  is  composed  of  a  smaller  and  a  larger 
thread,  the  former  turning  upwards  while  the  latter  turns  downwards 
with  a  little  greater  velocity,  and  consequently  the  screw,  on  the 
whole,  advances  with  the  difference  between  the  larger  and  the  small- 
er threads ;  and  since  this  difference  .may  be  small  to  any  extent,  so 
the  efficacy  of  the  power  may  be  increased  indefinitely.  It  will  be 
seen,  however,  that  the  motion  of  such  a  Fig  47 

screw  is  exceedingly  slow.     Thus,  in  fig-       ^^ 

ure  47,  A  descends,  while  B,  playing  in  a 
concave  screw  in  A,  ascends ;  but  the  dis- 
tance between  the  threads  of  A  being  great- 
er than  the  distance  between  those  of  B,  the 
screw,  on  the  whole,  advances  with  the  dif- 
ference. Suppose  that  A  has  20  threads 
in  an  inch  and  B  21 ;  then  during  one  rev- 
olution, A  will  descend  through  the  20th, 
while  B  ascends  through  the  21st  part  of  an 
inch.  The  compound  screw,  therefore,  will  advance  through  a 
space  -oqual  to  the  difference ;  that  is,  through  a  space  equal  to  ^V  — 
,_iT=_.i-th  of  an  inch.  This  small  space  is  therefore,  in  effect,  the 
distance  between  two  contiguous  threads ;  and  the  power  of  the  ma- 
chine is,  as  usual,  expressed  by  the  number  of  times  their  distance 


*      MACHINERY.  87 

is  contained  in  the  circumference  described  in  one  revolution  of  the 
power.  For  example,  let  the  circumference  of  the  circle  be  one 
foot;  then  12-~¥io=5040=  the  weight  or  resistance,  the  power 
being  1 ;  or,  in  other  words,  the  efficacy  of  the  power  is  increased 

five  thousand  and  forty  times. 

• 

174.  It  is  obvious,  however,  from  principles  already  explained, 
that  the  power  will  in  this  case  move  over  5040  times  as  great  a  space 
as  the  weight.     It  is  on  this  principle  that  the  Screw  affords  the 
means  of  measuring  very  minute  spaces,  and  hence  is  derived  the 
Micrometer  Screw.     The  very  slow  motion  which  may  be  imparted 
to  the  end  of  a  screw,  while  the  power  moves  over  a  space  vastly 
greater,  renders  it  peculiarly  adapted  to  this  purpose.     For  example, 
suppose  a  screw  to  be  so  cut  as  to  have  50  threads  in  an  inch :  then 
each  revolution  of  the  screw  will  advance  its  point  through  the  50th 
part  of  an  inch,   and  if  that  point  acted  against  a  thread  or  wire,  it 
would  move  it  over  a  graduated  space  only  that  distance  in  a  whole 
revolution  of  the  screw.     Now  suppose  the  head  of  the  screw  to  be 
a  circle  an  inch  in  diameter,  and  of  course  something  more  than  three 
inches  in  circumference.     This  circumference  may  easily  be  divided 
into  a  hundred  equal  parts,  distinctly  visible ;  and  if  a  fixed  index  be 
applied  to  it,  the  hundredth  part  of  a  revolution  of  the  screw  maybe 
observed,  by  noting  the  passage  of  one  division  of  the  head  under 
the  index.     But  the  hundredth  part  of  a  revolution  carries  the  point 
of  the  screw  only  through  the  (Ti7  of  I1-  =  )J^-th  part  of  an  inch. 
Such  an  apparatus  is  frequently  attached  to  the  limbs  of  graduated 
instruments,  for  the  purposes  of  astronomical  and  other  observations ; 
by  which  means,  a  potion  of  the  graduated  are  no  greater  than  the 
100th  part  of  a  second,  can  be  estimated. 

In  like  manner,  any  other  small  space  may  be  measured  by  the  aid 
of  the  Micrometer  Screw.  Thus,  any  aliquot  part  of  a  pound,  or  an 
ounce,  in  the  steelyards,  may  be  found  by  adapting  the  screw  to  the 
counterpoise  so  as  to  move  it  slowly  over  the  space  between  two 
notches,  and  at  the  same  time  point  out,  by  an  index  on  its  head,  the 
exact  portion  of  the  space  over  which  it  passes. 

I      4ft 

175.  Several  of  the  mechanical  powers  are  frequently  combined 
in  the  same  machine.     The  manner  in  which  this  is  done  is  exem- 
plified in  the  figure  annexed  to  the  following  problem. 


88 


MECHANICS. 


Fig.  48. 


A  shipwright  wishing  to'  haul  a  ship  upon  the  stocks,  employed  a 
machine,  combining  the  lever,  the  screw,  the  wheel  and  axle,  the 
pulley,  and  the  inclined  plane,  as  represented  in  the  annexed  dia- 
gram. 

The  handle  of  the 
winch  BCs=18  inches. 

The  distance  of  the 
threads  on  CD=1  inch. 

The  diameter  -of  the 
wheel  ED =4  feet. 

The  diameter  of  the 
axle  EF=lfoot. 

G  is  a  fixed,  and  H 
a  movable  pulley,  the 
number  of  strings  =4. 

Height  of  the  plane  equals  half  its  length. 

Allowing  a  man  to  turn  on  the  handle  B  with  a  power  equal  to 
100  Ibs.,  how  much  force  could  he  exert  on  the  ship? 

By  Art.  171.  100  Ibs.  exerted  at  B  would  become, 
atD,  11309.76 

And  since  the  diameter  of  the  wheel  is  four  times 
that  of  the  axle,  X  4 


Again,  this  is  rendered  fourfold  by  the  four  strings  of 
the  pulley, 

f 

Finally,  this  is  doubled  by  the  plane, 


45239.04 


180956.16 
2 


361812.32 

Hence,  the  force  exerted  on  the  ship  would  amount  to  more  than 
361812  Ibs.,  or  more  than  161 J  tons. 

THE    WEDGE. 

*> 

176.  If  instead  of  moving  a  load  on  an  inclined  plane,  the  plane 
itself  is  moved  beneath  the  load,  it  then  becomes  a  Wedge.  Thus, 
if  a  perpendicular  beam  have  one  end  resting  upon  an  inclined  plane, 
(the  beam  being  so  secured  as  to  be  capable  of  moving  only  up  and 


MACHINERY. 


89 


down,)  and  the  plane  be  drawn  under  it,  the  beam  will  be  elevated; 
and  the  power  required  to  effect  this  will  be  to  that  required  to  raise 
the  beam  when  applied  directly  to  it,  as  the  height  of  the  plane  to 
its  length : — or,  considering  the  plane  as  a  half  wedge,  the  propor- 
tion will  be,  as  half  the  back  of  the  wedge  to  its  length. 

111.  In  the  arts  and  manufactures,  wedges  are  used  where  an 
enormous  force  is  to  be  exerted  through  a  very  small  space.  Thus 
it  is  resorted  to  for  splitting  masses  of  timber  or  stone.  Ships  are 
raised  in  docks  by  wedges  driven  under  their  keels.  The  wedge  is 
the  principal  agent  in  the  oil  mill.  The  seeds  from  which  the  oil  is 
to  be  extracted  are  introduced  into  hair  bags,  and  placed  between 
planes  of  hard  wood.  Wedges  inserted  between  the  bags  are  driv- 
en by  allowing  heavy  beams  to  fall  on  them.  The  pressure  thus 
excited  is  so  intense,  that  the  seeds  in  the  bags  are  formed  into  a 
mass  nearly  as  solid  as  wood.  Instances  have  occurred  in  which 
the  wedge  has  been  used  to  restore  a  tottering  edifice  to  its  perpen- 
dicular position.  All  cutting  and  piercing  instruments,  such  as  knives, 
razors,  scissors,  chisels,  nails,  pins,  needles,  awls,  &c.  are  wedges. 
The  angle  of  the  wedge,  in  these  cases,  is  more  or  less  acute,  accord- 
ing to  the  purpose  to  which  it  is  applied.  In  determining  this,  two 
things  are  to  be  considered — the  mechanical  power,  which  is  increas- 
ed by  diminishing  the  angle  of  the  wedge ;  and  the  strength  of  the 
tool,  which  is  always  diminished  by  the  same  cause.  There  is, 
therefore,  a  practical  limit  to  the  increase  of  the  power,  and  that 
degree  of  sharpness  only  is  to  be  given  to  the  tool,  which  is  consist- 
ent with  the  strength  requisite  for  th6  purpose  to  which  it  is  to  be 
applied.  In  tools  intended  for  cutting  wood,  the  angle  is  generally 
about  30°;  for  iron  it  is  from  50°  to  60°;  and  for  brass,  from  80° 
to  90°.  Tools  which  act  by  pressure  may  be  made  more  acute 
than  those  which  are  driven  by  a  blow;  and,  in  general,  the  softer 
and  more  yielding  the  substance  to  be  divided  is,  and  the  less  the 
power  required  to  act  upon  it,  the  more  acute  the  wedge  may  be 
constructed. 

178.  In  many  cases,  the  utility  of  the  wedge  depends  on  that  which 
is  entirely  omitted  in  the  theory,  viz.  the  friction  which  arises  between 
its  surface  and  the  substance  which  it  divides.  This  is  the  case  when 

12 


90  MECHANICS. 

pins,  bolts,  or  nails,  are  used  for  binding  the  parts  of  structures  to- 
gether ;  in  which  case,  were  it  not  for  the  friction,  they  would  recoil 
from  their  places  and  fail  to  produce  the  desired  effect.  Even  when 
the  wedge  is  used  as  a  mechanical  engine,  the  presence  of  friction  is 
absolutely  indispensable  to  its  practical  utility.  The  power  generally 
acts  by  successive  blows,  and  is  therefore  subject  to  constant  inter- 
mission, and  but  for  the  friction,  the  wedge  would  recoil  between  the 
intervals  of  the  blows  with  as  much  force  as  it  had  been  driven  for- 
ward, and  the  object  of  the  labor  would  be  continually  frustrated. 

179.  The  following  principle  is  of  great  importance  in  relation  to 
all  the  mechanical  powers,  and  deserving  of  particular  attention. 

In  each  of  the  mechanical  powers,  and  in  every  machine,  the  power 
and  weight  balance  each  other,  when  the  power  moves  as  much  faster 
than  the  weight  as  its  quantity  of  matter  is  less. 

We  can,  therefore,  make  a  small  power  raise  a  very  great  weight, 
by  so  connecting  it  with  the  weight,  as  to  make  it  move  over  a  very 
great  space  while  the  weight  moves  over  a  very  small  space.  By 
reviewing  the  several  mechanical  powers,  we  shall  recognize  the 
operation  of  this  principle  in  each  of  them. 

180.  In  levers  of  the  first  and  second  kind,  (Figs.  20,  22.)  the 
power  being  applied  at  the  extremity  of  the  longer  arm  and  farther 
from  the  fulcrum  than  the  power,  moves  over  a  proportionally  great- 
er space  as  the  lever  turns  on  its  fulcrum ;  but  in  the  lever  of  the 
third  kind,  (Fig.  23.)  the  power  being  applied  nearer  the  fulcrum 
than  the  weight,  moves  with  less  velocity  than  the  weight,  and  con- 
sequently acts  under  a  mechanical  disadvantage,  and  requires  to  be 
proportionally  greater  than  the  weight. 

181.  In  the  wheel  and  axle,  (Fig.  31.)  as  both  the  wheel  and  its 
axle  revolve  in  the  same  time,  it  is  obvious  that  the  power  applied  at 
the  circumference  of  the  wheel  must  move  as  much  faster  than  the 
weight,  »g  the  circumference  of  the  wheel  is  greater  than  that  of  the 
axle.  , 

182.  In  the  pulley,  when  the  rope  merely  passes  over  a  fixed 
pulley,  (as  in  Fig.  40.)  the  power  and  weight  move  over  the  same 


MACHINERY.  91 

space,  and  no  mechanical  force  is  either  gained  or  lost ;  but  in  the 
movable  pulleys  represented  in  figure  24,  the  strings  that  raise  the 
weight  are  equally  shortened,  and  the  power  is  lengthened  by  an 
amount  equal  to  that  by  which  the  several  pahs  are  shortened  ; 
consequently,  the  power  moves  as  much  faster  than  the  weight  as  the 
number  of  ropes  is  greater  than  unity.  When  the  number  of  mova- 
ble pulleys  is  great,  the  great  space  over  which  the  power  must  move 
in  order  to  raise  the  weight  over  a  comparatively  small  space,  presents 
a  practical  inconvenience. 

183.  In  the  inclined  plane,  the  greater  the  length  of  the  plane  in 
proportion  to  its  height,  the  slower  will  be  the  perpendicular  ascent 
of  the  weight.     For  example,  if  the  length  of  the  plane  be  twice 
its  height,  the  power  must  move  over  twice  the  space,  as  it  would  if 
it  rose  perpendicularly,  and  hence  the  mechanical  advantage  gained 
is  in  the  same  ratio,  that  is,  the  power  required  is  so  much  less  than 
the  weight. 

184.  In  the  screw,  while  the  power  performs  one  complete  revo- 
lution, the  weight  is  elevated  only  the  distance  between  two  contigu- 
ous threads.     Hence,  when  the  power  is  applied  at  the  end  of  a  long 
lever,  and  the  distance  between  two  contiguous  threads  is  small,  the 
forward  motion  of  the  screw  is  very  slow,  while  the  power  traverses 
a  great  space. 

185.  In  a  combination  of  the  mechanical  powers,  such  as  that 
represented  in  Fig.  48,  we  see  the  same  principle  very  strikingly 
exhibited.     Here  the  power  moves  3619  times  as  fast  as  the  weight, 
and  the  mechanical  advantage  gained  is  in  the  same  ratio. 

186.  Finally,  in  the  wedge,  the  power  of  overcoming  resistances 
is  proportioned  to  the  acuteness  of  the  wedge ;  and  the  distance  to 
which  the  parts  are  separated,  that  is,  the  space  over  which  the 
weight  moves,  when  compared  with  the  space  through  which  the 
power,  (namely,  the  wedge  itself  in  the  direction  of  the  power,) 
moves,  is  constantly  diminished  as  the  acuteness  of  the  wedge  is  in- 
creased. 


92  MECHANICS. 

CHAPTER  XI. 

MACHINERY  CONCLUDED. 

187.  Archimedes  is  said  to  have  boasted  to  King  Hiero,  that  "  if 
he  would  give  him  a  place  to  fix  his  machine,  (tfoo  tf7w,)  he  would 
move  the  world."     Yet  there  can  be  no  machine  by  the  aid  of 
which  Archimedes  could  move  the  world,  in  any  other  way,  than  by 
moving,  himself,  over  as  much  more  space  than  that  over  which  he 
moved  the  earth,  as  his  weight  was  less  than  that  of  the  whole  earth. 
If  Archimedes  had  received  the  place  he  desired,  and  had  also  em- 
ployed what  was  equally  indispensable,  a  machine  which  operated 
free  of  all  resistance,  he  must  have  moved  with  the  velocity  of  a 
cannon  ball,  to  have  shifted  the  earth  only  the  twenty  seven  millionth 
part  of  an  inch  in  a  million  of  years. 

188.  From  the  foregoing  principles  it  will  be  inferred,  that  no  mo- 
mentum, or  effective  force  is  gained  by  any  of  the  mechanical  pow- 
ers, or  by  any  machine.     If  a  man  with  his  naked  hands,  can  lift  to 
a  given  height,  as  one  foot,  only  150  pounds  in  one  second,  it  is  im- 
possible for  him  to  perform  any  more  labor  than  this  by  any  mechan- 
ical contrivances.     On  the  contrary,  when  the  structure  of  the  ma- 
chine is  complicated,  there  is  a  loss  of  force,  by  employing  the  ma- 
chine instead  of  the  naked  hands,  proportioned  to  the  resistance  of 
the  parts  of  the  machine  itself.     It  is  to  be  remarked,  however,  that 
this  doctrine  proceeds  on  the  supposition  that  the  useful  effect  produ- 
ced is  estimated  from  the  joint  product  of  the  force,  velocity  and 
time.     A  convenient  method  of  estimating  different  forces  is  to  draw 
a  heavy  weight  out  of  a  well,  by  a  rope  passing  horizontally  over  a 
fixed  pulley,  near  the  top  of  the   well.     Suppose  that  a  man   can 
draw  up  a  rock  weighing  100  Ibs.  through  the  space  of  50  feet  in  one 
minute.     He  would,  of  course,  be  able  to  draw  up  ten  such  masses 
in  ten  minutes,  weighing  in  all  1000  pounds.     Now  by  passing  the 
rope  over  five  pulleys,  (allowing  nothing  for  the  friction  of  the  pull- 
eys,) he  might  with  the  same  force  lift  the  whole  1000  pounds  at  once, 
but  it  would  rise  ten  times  as  slowly  as  the  100  pounds  did  before, 
and  consequently  would  be  ten  minutes  in  reaching  the  top.     There- 
fore, in  a  given  time,  it  appears  that  the  man  would   raise  the  same 
weight  through  a  given  space,  with  or  without  the  aid  of  machinery. 


MACHINERY.  93 

In  the  former  case,  the  100  Ibs.  might  have  been  raised  during  the 
ten  minutes  through  the  space  of  500  instead  of  50  feet;  but 
100X500X10=1000X50X10;  so  that  the  labor  performed  would 
have  been  the  same  in  both  cases.  Let  us  suppose  that  P  is  a  pow- 
er amounting  to  an  ounce,  and  that  W  is  a  weight  amounting  to  50 
ounces,  and  that  P  elevates  W  by  means  of  a  machine.  In  virtue 
of  the  property  already  stated,  it  follows,  that  while  P  moves  through 
50  feet,  W  will  be  moved  through  1  foot;  but  in  moving  P  through 
50  feet,  fifty  distinct  efforts  are  made,  by  each  of  which,  if  applied 
directly,  1  ounce  would  be  moved  through  1  foot. 

189.  What  then,  it  may  be  asked,  are  the  advantages  gained  by 
Machinery1?  The  advantages  are  still  very  great,  for  the  following 
reasons. 

(1.)  By  the  aid  of  machinery  we  can  frequently  apply  our  force 
to  much  better  purpose.  Thus  in  lifting  a  weight  out  of  a  well,  or  in 
raising  ore  out  of  a  mine,  it  is  obvious  with  how  much  more  effect  a 
man  can  work  at  the  arm  of  a  windlass  than  he  could  draw  directly 
upon  the  rope  stooping  over  the  well.  So  in  raising  a  rock  from  its 
bed  by  means  of  a  handspike  or  crowbar,  we  can  easily  see  bow  much 
more  effectually  we  can  bring  our  force  to  bear  upon  it  than  we  could 
do  by  our  naked  hands. 

(2.)  By  the  aid  of  machinery,  a  man  may  be  able  to  perform 
works  to  which  his  naked  strength  would  be  wholly  incompetent. 
Thus,  as  in  the  preceding  exanmple,  one  might  be  able  to  lift  a  rock 
from  its  bed  with  a  handspike  upon  which  he  could  make  no  im- 
pression with  his  naked  hands ;  or,  by  means  of  pulleys,  he  might 
raise  a  box  of  merchandize  from  the  hold  of  a  ship,  which  he  could 
not  start  at  all  with  riis  unassisted  force.  In  each  of  these  cases,  if 
the  weight  could  be  divided  into  small  parcels,  and  if  the  force  could 
be  as  advantageously  applied  without  machinery  as  with  it,  the  labor 
would  be  performed  as  easily  in  a  given  time  in  one  way  as  in  the 
other.  But  it  might  not  be  possible  or  at  least  convenient  thus  to 
divide  it.  Or  if,  instead  of  dividing  it  into  a  number  of  parcels,  the 
same  number  of  men  could  act  directly  upon  a  weight  at  once,  the 
amount  of  labor  which  they  would  all  exert  in  raising  the  weight 
without  machinery,  would  be  the  same  as  that  which  the  single  man 
before  supposed  would  exert  with  his  machinery.  But  it  might  not 


94  MECHANICS. 

be  convenient  to  assemble  so  many  hands  at  a  time  ;  or  perhaps  such 
a  number  could  not  work  advantageously  together.  A  farmer  has 
many  occasions  for  lifting  or  removing  great  weights  when  his  labor- 
ers are  not  more  in  number  than  two  or  three  in  all.  These  must 
therefore  perform  the  labor  of  50  times  as  many  men  by  being  50 
times  as  long  about  it.  Thus,  in  the  example  given  on  page  88,  of 
a  combination  of  the  mechanical  powers  employed  to  haul  a  ship  on 
the  stocks,  where  a  single  man  turning  on  a  winch,  with  the  force  of 
100  Ibs.  exerts  a  force  on  the  ship  amounting  to  161 J  tons,  the  ship 
would  move  as  much  slower  than  the  hand  as  100  Ibs.  is  less  than 
161 J  tons;  and  consequently  a  great  length  of  time  would  be  re- 
quired for  an  individual  to  perform  this  labor,  even  supposing  no 
resistance  were  encountered  from  the  machinery  itself. 

(3.)  Machinery  frequently  enables  a  man  to  exert  his  whole  force 
in  circumstances  where,  without  such  aid,  he  could  employ  but  a  part 
of  it.  Thus,  in  winding  silk  or  thread,  to  turn  a  single  reel  might 
not  require  one  fiftieth  part  of  the  force  which  the  laborer  was  capa- 
ble of  exerting.  Suitable  machinery  would  enable  him  to  turn  fifty 
spools  at  once. 

(4.)  But  the  most  striking  advantage  of  Machinery  is  not  found 
in  the  facilities  which  it  lends  to  the  personal  strength  of  man  :  It 
lies  in  this,  that  it  affords  the  means  of  calling  in  to  his  assistance  the 
superior  powers  of  the  horse  and  the  ox,  of  water,  of  wind,  and  es- 
pecially of  steam.  Here  we  find  the  excellence  of  mechanical  con- 
trivances fully  exhibited  ;  and  no  where  else  has  the  inventive  genius 
of  man  displayed  itself  to  so  great  advantage.  But  here,  as  in  all 
other  cases,  the  various  combinations  of  mechanical  powers  produce 
no  force  :  kthey  only  apply  it.  They  form  the  communication  be- 
tween the  moving  power  and  the  body  moved ;  and  while  the  power 
itself  may  be  incapable  of  acting  except  in  one  direction,  we  are  able, 
by  means  of  cranks,  levers  and  toothed  wheels,  to  direct  and  modify 
that  force  to  suit  our  convenience  or  necessities.  Every  one  may 
see  examples  of  this  in  the  construction  of  the  most  common  saw 
mill  or,  flour  mill,  turned  by  water.  In  a  mill  for  grinding  wheat, 
the  stones  are  required  to  move  horizontally,  while  the  action  of  the 
water  fall  is  perpendicular.  We  there'fore  receive  the  whole  force 
on  the  circumference  of  a  wheel,  and  transmit  it  through  several  in- 
termediate wheels  to  the  revolving  stone,  where  the  grinding  is  per- 


MACHINERY. 

formed.  So  in  a  saw  mill,  the  water  first  communicates  a  rotary 
motion  to  the  wheel,  and  this  motion  is  converted  by  means  of  a 
crank  into  what  is  called  a  reciprocating  motion,  as  that  of  the  saw 
in  its  ascent  and  descent.  By  means  of  wheel  work  the  velocity  o-f 
the  moving  body  is  increased  or  diminished  at  pleasure. 

190.  In  short,  machines  enable  us  to  form  a  convenient  communi- 
cation between  the  power  and  the  weight ;  to  give  to  the  weight  any 
required  direction  or  velocity  ;  to  apply  force  to  the  best  advantage ; 
to  vary  the  circumstances  of  velocity  and  time  as  the  amount  of  our 
force  may  require  ;  and  to  bring  to  our  aid  the  great  moving  powers 
that  exist  in  nature.     Our  next  object,   therefore,  will  be  to  see  by 
what  particular  methods,  these  several  purposes  are  accomplished. 

Regulation  of  Machinery,  and  Contrivances  for  Modifying  Motion. 

191.  It  is  highly  important  to  the  successful  operation  of  any  ma- 
chine, that  its  motion  should  be  regular  and  uniform.     Jolts  and  ir- 
regular movements  waste  the  power,  wear  upon  the  machine,  and 
perform  the  work  unevenly.     The  sources  of  irregularity  are  vari- 
ous,  but   they  are  chiefly  the  three  following,  viz.  variations  in  the 
power,  variations  in  the  weight  or  resistance,  and  changes  of  veloci- 
ty in  parts  of  the  machine  itself.     Thus  in  the  steam  engine,  the  fire 
may  burn  with  more  or  less  intensity  and  produce  corresponding  quan- 
tities of  the  moving  power ;  the  load  to  be  carried  (as  that  of  a  steam 
boat,)  may  be  much  greater  at  one  time  than  at  another,  and  be  sub- 
ject to  sudden  changes ;  and  the  motion  of  the  piston,  which  carries 
the  machinery,  ceases  altogether  at  the  highest  and  lowest  points, 
and  would  move  a  machine  by  hitches  or  separate  impulses,  were 
there  no  contrivance  connected  with  it  for  keeping  up  a  uniform  mo- 
tion. 

192.  The  kinds  of  apparatus  employed  to  obviate  these  difficul- 
ties,  and  to  secure  uniform  movements  to  machines,  are,  in  general 
called  REGULATORS.     Large  machines  or  engines  themselves,  in  con- 
sequence of  their  inertia,  acquire  and  maintain,  to  a  considerable  ex- 
tent, uniformity  of  motion.     A  flour  mill  carried  by  water,  when  it 
has  acquired^  certain  rate  of  going,   will  not  suddenly  change  that 
rate  by  any  alteration  in  the  force  of  the  stream ;  and  a  ship  sailing 


96 


MECHANICS. 


49. 


between  the  opposite  forces,  arising  from  the  impulse  of  the  wind 
and  the  resistance  of  the  water  will  move  steadily  along,  notwithstand- 
ing the  breeze  that  carries  it  snay  fluctuate  continually.  We  can  see 
this  principle  sometimes  operating  on  a  smaller  scale.  A  grindstone 
turned  by  a  winch  moves  steadily,  although  the  force  applied  at  one 
part  of  the  revolution  is  much  greater  than  at  another.  Large  grind- 
stones exhibit  the  advantage  of  this  principle  much  more  than  small 
ones.  But  in  many  instances,  this  natural  tendency  towards  uniform 
motion  is  not  sufficient,  and  artificial  contrivances  are  introduced  ex- 
pressly for  this  purpose.  As  examples  of  Regulators  we  may  espe- 
cially notice  two,  the  Pendulum,  and  the  Fly  Wheel. 

193.  The  Pendulum,  by  its  equal  vibrations,  communicates  to  del- 
icate machinery  a  motion  extremely  regular,  and  hence  its  applica- 
tion to  the  measurement  of  time. 

The  Fly  Wheel,  affords  the  most  common  and  effectual  method  of 
equalizing  motion,  especially  in  heavy 
kinds  of  machinery.  It  consists  of  a 
heavy  wheel  (Fig.  49,)  affording  as  much 
weight  as  possible  under  as  small  a  sur- 
face, in  order  that  the  inertia  may  be 
great  while  the  resistance  from  the  air  is 
small.  It  is  therefore  usually  a  heavy 
hoop  of  iron  with  thick  bars  of  the  same 
metal.  The  Fly  is  balanced  on  its  axis, 
and  so  connected  with  the  machinery  as  to 
turn  rapidly  around  with  it,  and  receiving 
a  constant  impulse  from  the  moving  power,  it  becomes  a  magazine 
or  repository  of  motion.  Consequently,  by  its  inertia,  it  is  ready  to 
supply  any  deficiency  of  power  that  may  arise  from  the  sudden  dim- 
inution of  the  moving  force  or  to  check  any  sudden  impulse  which 
may  result  from  an  accidental  excess  of  that  force.  Suppose,  for 
example,  the  handle  of  a  pump  to  be  connected  with  a  water  wheel, 
and  to  be  carried  by  it.  Here  the  power,  namely  the  water  fall,  is 
constant,  while  the  weight  is  subject  to  continual  alternations,  amount- 
ing to  a  heavy  load  as  the  piston  is  ascending,  but  opposing  scarcely 
any  resistance  while  the  piston  is  descending.  The  motion,  there- 
fore, would  vary  between  nothing  and  a  highly  accelerated  velocity, 
and  the  machinery  would  be  subject  to  constant  strains  and  jolts.  A 


MACHINERY.  97 

Fly  prevents  these  alternations  and  renders  the  ascent  and  descent  of 
the  piston  nearly  uniform.  In  pile  engines  or  stamping  mills,  a  team 
of  horses  is  sometimes  employed  to  raise  a  heavy  weight,  which 
when  at  a  certain  elevation,  is  suddenly  disengaged  and  falls  with 
great  force.  As  the  disengagement  is  instantaneous,  the  horses 
would  instantly  tumble  down  were  not  their  motion  checked  by  some 
contrivance  which  should  prevent  the  machinery  from  receiving  any 
sudden  increase  of  velocity.  This  purpose  is  completely  answered 
by  the  Fly. 

194.  Beside  the  use  of  the  Fly  Wheel  in  regulating  the  action 
of  Machinery,  it  is  employed  for  the  purpose  of  accumulating  suc- 
cessive exertions  of  a  power  so  as  to  produce  a  much  more  forcible 
effect  by  their  aggregation,  than  could  possibly  be  done  by  their  sepa- 
rate actions.     If  a  small  force  be  repeatedly  applied  in  giving  rota- 
tion to  a  Fly  Wheel,   and  be  continued  until  the  wheel  has  acquired 
a  very  considerable  velocity,  such  a  quantity  of  force  will  be  at  length 
accumulated  in  its  circumference,  as  to  overcome  resistance  and  pro- 
duce effects  utterly  disproportionate  to  the  immediate  action  of  the 
original  force.     Thus  it  would  be  very  easy  in  a  few  seconds,  by  the 
mere  action  of  a  man's  arm,  to  impart  to  the  circumference  of  a  Fly 
Wheel,   a  force  which  would  give  an  impulse  to  a  musket  ball  equal 
to  that  which  it  receives  from  a  full  charge  of  powder. 

195.  The  same  principle  explains  the  force  with  which  a  stone 
may  be  projected  from  a  sling.     The  thong  is  swung  several  times 
around  by  the  arm  until  a  considerable  portion  of  force  is  accumu- 
lated,  and  then  it  is  projected  with  all  the  collected  force.     If  a 
heavy  leaden  ball  be  attached  to  the  end  of  a  strong  piece  of  cane  or 
whalebone,  it  may  easily  be  driven  through  a  board  :  by  taking  the 
end  of  the  rod  remote  from  the  ball  in  the  hand,  and  striking  the 
board  a  smart  blow  with  the  end  bearing  the  ball,  s'-xh  a  velocity  may 
easily  be  given  to  the  ball  as  will  drive  it  through  the  board. 

196.  The  astonishing  effects  of  a  Fly  Wheel,   as  an  accumulator 
of  force,  have  led  some  into  the  error  of  supposing  that  such  an  appa- 
ratus increases  the  actual  force  of  a  machine.     So  far  from  this,  since 
a  Fly  cannot  act  without  friction  and  resistance  from  the  air,  a  por- 
tion of  the  actual  moving  force  must  unavoidably  be  lost  by  the  use 

13 


98  MECHANICS. 

of  this  appendage.  In  cases,  however,  where  a  Fly  is  properly  ad- 
justed and  applied,  this  loss  of  power  is  inconsiderable,  compared 
with  the  advantageous  distribution  of  what  remains.  As  an  accu- 
mulator of  force,  a  Fly  can  never  have  more  force  than  has  been 
applied  to  put  it  in  motion.  In  this  respect  it  is  analogous  to  an  elas- 
tic spring.  la  bending  a  spring,  a  gradual  expenditure  of  power  is 
necessary.  On  the  recoil,  this  power  is  exerted  in  a  much  shorter 
time  than  that  consumed  in  its  production,  but  its  total  amount  is  not 
altered*  In  this  way  the  Fly  Wheel  is  used.  Thus,  in  mills  for 
rolling  metal,  the  water  wheel  or  other  moving  power,  is  allowed 
for  some  time,  to  act  upon  the  Fly  alone,  no  load  being  placed  upon 
the  machine.  A  force  is  thus  gained  which  is  sufficient  to  roll  a 
large  piece  of  metal,  to  which,  without  such  means,  the  mill  would 
be  quite  inadequate.  In  the  same  manner,  a  force  may  be  gained 
by  the  arm  of  a  man  acting  on  a  Fly  for  a  few  seconds,  sufficient  to 
impress  an  image  on  a  piece  of  metal  by  an  instantaneous  stroke. 

197.  We  have  already  explained  the  mode  in  which  motion   is 
communicated,  and  its  velocity  regulated,  by  wheel  work.     We  pro- 
ceed now  to  consider  a  few  examples  of  the  more  special  contrivan- 
ces by  which  motion  is  modified  to  suit  particular  purposes,  recom- 
mending it  to  the  student  of  mechanics  to  make  himself  acquainted 
with  other  contrivances  of  the  same  nature,  by  the  actual  inspection 
of  machinery  as  opportunity  may  offer. 

198.  The  motion  required  for  a  particular  purpose  may  be  recti- 
linear as  that  of  a  carriage  or  bucket  drawn  out  of  a  well,  or  rotary 
as  in   ordinary  wheel  work,  or  reciprocating  as  in  a  saw  mill,  or  a 
pendulum. 

The  simplest  mode  of  producing  rectilinear  motion  is  by  means  of 
a  rope  or  chain,  instances  of  which  are  familiar  to  every  one.  The 
simplest  mode  of  changing  the  direction  is  by  means  of  pulleys ;  but 
toothed  wheels  are  also  extensively  employed  for  the  same  purpose. 
The  connexion  of  one  toothed  wheel  with  another  is  called  gearing. 
When  both  wheels  with  their  teeth  are  in  the  direction  of  the  same 
plane,  it  is  called  spur  gearing  (figs.  36.  7.  and  8.) ;  if  the  teeth,  in- 
stead of  being  cut  on  the  circumference  in  a  direction  parallel  to  the 
axis,  are  cut  obliquely,  so  that  if  continued  they  would  pass  round 


MACHINERY. 


the  axis  like  a  screw,  it  is  called  spiral  gearing  (Fig.  50.) ;  and  when 
wheels  are  not  situated  in  the  same  or  parallel  planes,  but  form  an 
angle  with  each  other,  the  wheels  themselves  are  sometimes  shaped 
like  frustums  of  cones,  having  their  teeth  cut  obliquely,  and  converg- 
ing toward  the  point  where  the  apex  of  the  cone  would  be  situated, 
and  it  is  th«i  called  bevel  gearing,  (Fig.  51.) 


Fig.  50. 


Fig.  51. 


Fig.  52. 


Fig.  53. 


199.  The  universal  joint  consists  of  two  shafts  or  arms,  each  ter- 
minating in  a  semicircle,  and  connected  together  by  means  of  a  cross 
upon  which  each  semicircle  is  hinged.  (Fig.  52.)  When  one  shaft 
is  turned,  either  to  the  right  or  left,  the  other  shaft  turns  in  the  same 
direction. 

The  ratchet  wheel  (Fig.  53.)  is  used  to  prevent  motion  in  one  di- 
rection while  it  permits  it  in  the  opposite.  The  teeth  are  cut  with 
their  faces  inclining  as  in  the  figure,  and  a  catch  is  so  placed  as  to 
stop  the  wheel  in  one  direction,  while  it  slides  over  the  teeth  without 
obstruction  in  the  opposite  direction. 


200.  The.  eccentric  wheel  (Fig.  54.)  revolves  about 
an  axis  which  is  more  or  less  removed  from  the  cen- 
ter, and,  consequently,  the  different  portions  of  the 
circumference  move  with  different  degrees  of  velo- 
city. Hence,  if  this  wheel  is  made  to  act  upon  a 
shaft  or  pinion,  as  in  the  figure,  it  will  carry  it  with  a 
corresponding  movement.  In  orreries,  such  wheels 
are  employed  for  indicating  the  variable  velocities  of 
the  heavenly  bodies,  as  they  revolve  about  their  cen- 
ters of  motion. 


Fig.  54. 


100  MECHANICS. 

201.  RECIPROCATING  MOTION  is  produced  in  various 
ways.  The  most  common  method  is  by  means  of  the 
crank.  In  figure  55,  a  shaft  AB  is  urged  backwards  or 
forwards,  (either  vertically  or  horizontally,)  by  means  of 
the  crank  ab,  moving  on  a  wheel  H,  which  may  be  turned 
by  water  or  any  other  power  acting  at  H.  By  consider* 
ing  the  different  positions  of  the  crank  during  the  revolu- 
tion  of  the  wheel,  it  will  be  readily  seen  that  the  shaft 
will  move  up  and  down  like  the  saw  in  a  saw  mill,  or 
backwards  and  forwards,  a  use  to  which  it  is  applied  in 
polishing  plane  surfaces,  as  marble. 

The  motion  produced  by  cranks  is  easy  and  gradual, 
being  most  rapid  in  the  middle  of  the  stroke,  and  gradu- 
ally retarded  towards  the  extremes  ;  so  that  shocks  and  jolts  in  the 
moving  machinery  are  diminished,  or  wholly  prevented  by  their  use. 


.  The  steam  engine,  as  seen  in  steam  boats,  furnishes  to  the 
student  of  Mechanics  a  valuable  opportunity  of  observing  various 
contrivances  for  producing,  regulating,  and  modifying  motion.  Lev- 
ers and  wheels  of  various  kinds  and  variously  connected  ;  fly  wheels 
and  cranks  ;  circular  and  reciprocating  motions  ;  and  numerous  oth- 
er particulars  which  appertain  to  the  "  elements  of  machinery,"  are 
there  seen  to  the  greatest  advantage, 


CHAPTER  XII. 

» 

OF  THE  PENPULUM,  OF  STRENGTH  OF  MATERIALS,  AND 
OF  FRICTION. 

The  Pendulum, 

203.  The  practical  application  of  the  Pendulum  to  three  most  im- 
portant objects,  namely,  the  measurement  of  time,  the  estimation  of 
the  figure  of  the  earth,  and  as  a  standard  of  weights  and  measures, 
renders  it  deserving  of  the  attention  of  students  of  Natural  Philosophy. 

204.  JL  Pendulum  is  a  body  suspended  by  a  right  line  from  any 
point,  and  moving  freely  about  that  point  as  a  center.     The  point 


PENDULUM, 


101 


about  which  the  pendulum  revolves,  is  called  the  center  of  suspen- 
sion. The  vibration  of  a  pendulum,  is  its  motion  from  a  state  of 
rest  at  the  highest  point  on  one  side,  to  the 
highest  point  on  the  other  side.  The  center 
of  oscillation  of  a  pendulum,  is  such  a  point 
that,  were  all  the  matter  of  the  pendulum  col- 
lected in  it,  the  quantity  of  motion  (or  mo- 
mentum) would  be  equal  to  the  sum  of  the 
momenta  of  all  the  parts  taken  separately. 
Thus,  the  parts  of  the  pendulum  about  6, 
(Fig.  56.)  move  faster  than  those  about  a,  and 
consequently  have  more  momentum ;  but  there 
is  a  point  about  which  the  momenta  balance 
each  other,  and  therefore,  in  the  investigations 
relating  to  the  pendulum,  all  the  parts  of  which 
it  consists  may  be  considered  as  concentrated 
in  that  point. 

The  center  of  oscillation  is  below  the  center  of  gravity;  for  since 
the  parts  more  remote  from  the  center  of  suspension  have  more  ve- 
locity than  the  parts  that  are  nearer  to  it,  the  quantity  of  matter  be- 
low the  center  of  oscillation  must  be  less  than  the  quantity  of  matter 
above  it. 


205.  The  doctrine  of  the  Pendulum  is  mainly  comprised  in  the 
following  propositions. 

A  pendulum  of  given  length,  performs  its  vibrations  in  equal  times, 
whether  it  vibrates  in  longer  or  in  shorter  arcs. 

Upon  this  property  of  the  pendulum,   depends  its  application  to 
the  measurement  of  time,  as  explained  in  Art.  152. 

206.  The  times  of  vibration  of  pendulums  of  different  lengths, 
are  proportioned  to  the  square  roots  of  their  lengths. 

Thus,  a  pendulum,  in  order  to  vibrate  half  seconds,  is  only  one 
fourth  as  long  as  one  that  vibrates  seconds,  for 

1  (the  time  of  the  longer)  :  J  (time  of  the  shorter) : :  VI  :  1/|. 


102  MECHANICS. 

What  must  be  the  length  of  a  pendulum  to  vibrate  quarter  seconds? 

Ans.  It  must  be  y1^  the  length  of  the  seconds  pendulum,  the  square 
root  of  yV  being  J  of  1 ;  and  since  the  length  of  a  pendulum  beat- 
ing seconds  is  about  39  inches,  that  of  a  pendulum  beating  quarter 
seconds,  is  ff  =2.44  nearly. 

Ex.  3.  What  would  be  the  length  of  a  pendulum  that  should  vi- 
brate once  an  hour,  the  length  of  the  seconds  pendulum  being  39T'-0- 
inches  ? 

Ans.  7997.7  miles,  equal  to  the  diameter  of  the  earth,  nearly. 

207.  The  times  of  vibration  of  the  same  pendulum  on  different 
parts  of  the  earth's  surface,  are  proportioned,  to  the  distances  of 
these  points  from  the  center  of  the  earth. 

Hence,  the  pendulum  affords  the  means  of  measuring  the  heights 
of  mountains,  and  even  of  ascertaining  the  figure  of  the  earth  itself. 
For,  since  the  times  of  vibration  are  as  the  respective  distances  from 
the  center  of  the  earth,  and  since  the  longer  the  time  occupied  in 
one  vibration,  the  smaller  the  number  of  vibrations  in  an  hour,  con- 
sequently, the  number  of  vibrations  in  an  hour  at  the  level  of  the 
sea  would  be  to  the  number  on  the  top  of  a  mountain,  as  the  dis- 
tance of  this  last  point  from  the  center  of  the  earth,  to  the  distance 
of  the  general  level  from  the  center. 

For  example,  a  pendulum  which  vibrated  seconds  at  the  level  of 
the  sea,  was  found  to  vibrate  only  3590  times  on  the  top  of  a  high 
mountain ;  what  was  the  height  of  the  mountain  ? 

3590  :  3600:  :3956*  :  3,969,  or  nearly  4  miles. 

Ex.  2.  A  pendulum  which  vibrated  seconds  at  the  general  level 
of  the  sea,  was  found  to  vibrate  but  3597  times  in  an  hour,  on  the 
top  of  a  neighboring  mountain  :  required  the  height  of  the  mountain? 

Ans.  3r\  miles. 

208.  Again,  the  pendulum  affords  us  the  means  of  ascertaining 
the  figure  of  the  earth ;  for  by  counting  the  number  of  vibrations 
perforn^ed  at  various  places  on  the  earth's  surface,  (at  the  level  of 
the  sea,)  we  determine  the  respective  distances  of  those  points  from 


*  The  diameter  of  the  earth  is  7912  miles. 


STRENGTH    OF    MATERIALS.  103 

the  center  of  the  earth.  Now,  if  these  distances"  should  be  all  equal 
to  each  other,  then  the  earth  would  be  found  to  be  a  perfect  sphere ; 
but  it  is  found,  by  actual  experiment,  that  the  number  of  vibrations 
increases  as  we  advance  from  the  equator  towards  the  poles,  indica- 
ting that  the  polar  diameter  is  less  than  the  equatorial. 

Example.    If  a  pendulum  which  beats  seconds  at  the  equator, 
should  be  found  to  vibrate  3613  times  in  an  hour  at  the  pole,  how 
much  less  is  the  polar  than  the  equatorial  diameter  ? 
3613  :  3600: : 4000  :  39S5TV 

This  result  being  subtracted  from  4000,  (the  equatorial  radius,) 
leaves  14,\  miles,  which,  being  doubled,  gives  28  fV  miles,  as  the 
difference  between  the  polar  and  equatorial  diameters. 

209.  The  fact  that  at  any  given  place,  a  pendulum  which  vibrates 
seconds,  or  which  makes  3600  vibrations  in  an  hour,  is  necessarily 
of  the  same  length  at  all  times,  has  led  several  nations  to  adopt  this 
as  the  standard  of  linear  measure.     The  square  of  this  will  serve 
as  a  standard  for  superficial,  and  its  cube  as  a  standard  for  solid 
measures. 

Strength  of  Materials. 

210.  The  importance  to  the  architect  and  the  engineer  of  ascer- 
taining the  form  and  position  of  the  materials  which  he  employs,  in 
order  to  secure  the  greatest  degree  of  strength  and   stability  at  the 
least  expense,  has  led  mathematicians  and  writers  on  mechanics,  to 
devote   much   attention  to  this  subject.     How  is  the  strength  of  a 
beam  affected  by  giving  to  it  different  shapes  and  different  positions; 
how  must  a  given  quantity  of  matter  be  disposed  of  in  order  that  it 
may  have  the  greatest  possible  degree  of  strength ;  and  upon  what 
principles  depends  the  stability  of  columns,  roofs,  and  arches  :  these, 
and  many  similar  inquiries,  have  been  objects  of  profound  investi- 
gation. 

211.  The  power  of  a  regular  beam,  like  a  stick  of  timber,  to  resist 
fracture  when  supported  horizontally  at  the  two  ends  is  proportioned 
to  the  depth  of  the  center  of  gravity  below  the  upper  surface.     Hence 
an  oblong  beam  is  much  stronger  with  its  narrow  than  with  its  broad 


104  MECHANICS. 

side   upwards,   as  will  be  seen  by  inspecting 

Fig.  57  ;  for  the  center  of  gravity  being  here 

the  center  of  the  stick,  its  depth  EG  is  greater 

when  the  narrow  side  is  uppermost  than  Eg, 

the  depth  when  the  beam  rests  on  its  broadside. 

Thus,  if  a  joist  be  10  inches  broad  and  2J 

thick,  it  will  bear  four  times  more  weight  when  B 

laid  on  its  edge,  than  when  laid  flat-wise.     Hence  the  modern  mode 

of  flooring  with  very  thin,  but  deep  pieces  of  timber. 

A  triangular  beam  is  twice  as  strong  when  resting  on  its  broad 
base,  as  when  resting  on  its  edge.  For  the  center  of  gravity  being 
|  the  distance  from  the  vertex  to  the  base,  its  depth  is  twice  as  great 
when  the  beam  rests  on  its  base  as  when  it  rests  on  its  edge.  These 
principles  apply  not  only  to  beams,  but  to  bars,  and  similar  struc- 
tures of  every  sort  of  matter. 

212.  The  strength  of  any  bar  in  the  direction  of  its  length  is  pro- 
portional to  the  area  of  its  transverse  section. 

If  a  number  of  cords  were  hanging  -side  by  side  from  the  same 
hook  in  the  ceiling  they  would  be  competent  to  sustain  a  weight  as 
much  greater  than  a  single  cord  would  sustain  as  their  number  was 
greater  than  unity.  Fifty  cords  all  bearing  equally,  would  obviously 
bear  fifty  times  as  great  a  weight  without  breaking  as  a  single  cord 
would  do.  Nor  would  their  power  be  altered  by  being  placed  close- 
ly in  contact  with  each  other  so  as  to  constitute  one  and  the  same  cord. 
If,  in  the  place  of  one  of  these  strings,  we  suppose  rows  or  particles  of 
any  kind  of  matter,  the  strength  of  the  whole  would  be  in  propor- 
tion to  their  number,  and  this  would  be  measured  by  the  area  of  a 
cross  section.  Hence,  the  various  shapes  of  bars  make  no  difference 
in  their  absolute  strength,  since  this  depends  only  on  the  area  of  the 
section,  and  must  obviously  be  the  same  when  the  area  is  the  same, 
whatever  be  the  figure.  A  rope,  therefore,  or  a  wire,  to  which  a 
weight  is  appended,  is  as  likely  to  break  in  one  place  as  in  another;, 
but  when  the  weight  of  the  rope  becomes  considerable,  and  the  force 
is  applied  perpendicularly,  the  increase  of  weight  as  its  length  increa- 
ses, renders  it  more  liable  to  break  in  the  upper  than  in  the  lower  parts. 

213.  The  lateral  strength  of  a  beam  is  inversely  as  its  length- 


STRENGTH    OF    MATERIALS.  105 

Hence  a  beam  twice  as  long  as  another  equal  to  it  in  all  other  re- 
spects, has  only  half  the  strength.  Long  beams  are  weak  from  their 
own  weight ;  and  the  length  may  be  so  increased,  that  they  will 
break  from  this  cause  alone. 

214.  The  tendency  to  fracture  on  any  part  of  a  horizontal  learn 
supported  at  both  ends,  is  proportional  to  the  product  of  the  distan- 
ces of  that  part  from  the  supported  ends. 

In  a  common  stick  of  timber,  therefore,  resting  horizontally  like 
the  joist  of  a  floor,  the  liability  to  break  is  greatest  in  the  middle,  and 
decreases  both  ways  to  the  ends ;  for  the  product  of  the  two  halves 
is  the  greatest  that  can  result  "from  any  two  parts,  and  the  more  un- 
equal the  parts  are,  the  less  is  the  product.  Hence  a  beam,  in  order 
to  be  equally  strong  throughout  must  be  made  tapering,  being  largest 
in  the  center,  and  growing  less  and  less  towards  the  ends.  Exact 
calculation  shows,  that  the  true  figure  of  such  a  beam  is  that  whose 
section  is  an  ellipse. 

The  timbers  which  compose  the  horizontal  part  of  the  frame  of  a 
house,  being  usually  rectangular  parallelopipeds  of  uniform  dimen- 
sions thoughout,  it  is  manifest  that  a  considerable  portion  of  the  ma- 
terial is  wasted  :  but  in  such  cases  the  attempt  to  save  the  material, 
would  be  attended  with  paramount  disadvantages.  When,  however, 
the  material  is  expensive,  or  where  lightness  is  important,  as  in  many 
kinds  of  machinery,  the  foregoing  principle  may  be  applied  with 
great  advantage.  A  useful  application  of  it  is  seen  in  the  shape  giv- 
en to  the  iron  bars  of  railways,  as  is  represented  in  the  following  figure. 

Fig.  58. 


215.  On  the  foregoing  principles  Dr.  Gregory  makes  the  follow- 
ing remarks,  most  of  which  were  originally  suggested  by  Galileo,  to 
whom  we  are  indebted  for  the  earliest  investigation  of  these  proposi- 
tions. From  the  preceding  deduction  (says  Gregory)  it  follows, 
that  greater  beams  and  bars  must  be  in  greater  danger  of  breaking 
than  less  similar  ones ;  and  that,  though  a  less  beam  may  be  firm 

14 


106  MECHANICS. 

and  secure,  yet  a  greater  similar  one  may  be  made  so  long  as  neces- 
sarily to  break  by  its  own  weight.  Hence  Galileo  justly  concludes, 
that  what  appears  very  firm,  and  succeeds  well,  in  models,  may  be 
very  weak  and  unstable,  or  even  fall  to  peices  by  its  weight,  when  it 
comes  to  be  executed  in  large  dimensions,  according  to  the  model. 
From  the  same  principles  he  argues  that  there  are  necessarily  limits 
in  the  works  of  nature  and  art,  which  they  cannot  surpass  in  magni- 
tude ;  that  immensely  great  ships,  palaces,  temples,  &tc.,  cannot  be 
erected,  since  their  yards,  beams,  bolts,  and  other  parts  of  their 
frame,  would  fall  asunder  by  their  own  weight.  Were  trees  of  a 
very  enormous  magnitude,  their  branches  would,  in  like  manner,  fall 
off.  Large  animals  have  not  strength  in  proportion  to  their  size  ; 
and  if  there  were  any  land  animals  much  larger  than  those  we  kjiow, 
they  could  hardly  move,  and  would  be  perpetually  subjected  to  the 
most  dangerous  accidents.  As  to  marine  animals,  indeed,  the  case 
is  different,  as  the  specific  gravity  of  the  water  sustains  those  ani- 
mals in  a  great  measure  ;  and  in  fact  these  are  known  to  be  some- 
times vastly  larger  than  the  greatest  land  animals.*  It  is  (says 
Galileo)  impossible  for  Nature  to  give  bones  to  men,  horses,  or  other 
animals,  so  formed  as  to  subsist,  and  proportionally  to  perform  their 
offices,  when  such  animals  should  be  enlarged  to  immense  heights, 
unless  she  uses  matter  much  firmer  and  more  resisting  than  she  com- 
monly does  ;  or  should  make  bones  of  a  thickness  out  of  all  propor- 
tion ;  whence  the  appearance  and  figure  of  the  Animal  must  be  mon- 
strous. Hence  we  naturally  join  the  idea  of  greater  strength  and 
force  with  the  grosser  proportions,  and  that  of  agility  with  the  more 
delicate  ones.  The  same  admirable  philosopher,  likewise  remarks, 
in  connexion  with  this  subject,  that  a  greater  column  is  in  much 
more  danger  of  being  broken  by  a  fall  than  a  similar  small  one  ;  that 
a  man  is  in  greater  danger  from  accidents  than  a  child  ;  that  an  in- 
sect can  sustain  a  weight  many  times  greater  than  itself,  whereas,  a 
much  larger  animal,  as  a  horse,  could  scarcely  carry  another  horse 
of  his  own  size. 


216.  5%e  lateral  ,  strengths  of  two  cylinders,  of  the  same  matter  y 
and  of  equal  weight  and  length,  one  of  which  is  hollow  and  the  oth- 
er solid,  are  to  each  other  as-  the  diameters  of  their  sections. 

*  Whales  in  the  Northern  Regions,  are  sometimes  found  sixty  feet 
long,  and  weighing  seventy  tons.' 


FRICTION. 


107 


The  strongest  form,  therefore,  in  which  a  given  quantity  of  mat- 
ter can  be  disposed,  is  that  of  a  hollow  cylinder.  From  this  propo- 
sition Galileo  justly  concludes,  that  Nature  in  a  thousand  operations 
greatly  augments  the  strength  of  substances  without  increasing  their 
weight;  as  is  manifested  in  the  bones  of  animals,  and  the  feathers  of 
birds,  as  well  as  in  most  tubes  or  hollow  trunks,  which,  though  light, 
greatly  resist  any  effort  to  bend  them.  Thus  (says  he)  if  a  wheat 
straw,  which  supports  an  ear  which  is  heavier  than  the  whole  stalk, 
were  made  of  the  same  quantity  of  matter,  but  solid,  it  would  bend 
or  break  with  far  greater  ease  than  it  now  does.  And  with  the  same 
reason,  art  has  observed,  and  experience  confirmed  the  fact,  that  a 
hollow  cane,  or  tube  of  wood  or  metal,  is  much  stronger  or  firmer, 
than  if,  while  it  continues  of  the  same  weight  and  length,  it  were  sol- 
id ;  as  it  would  then,  of  consequence,  be  not  so  thick.  For  the  same 
reason,  lances,  when  they  are  required  to  be  both  light  and  strong, 
are  made  hollow. 

Friction. 

217.  The  term  Friction,  in  its  usual  acceptation,  being  generally 
understood,  we  have  already  employed  it  in  the  foregoing  pages,  but 
we  proceed  now  to  inquire  more  particularly  respecting  its  nature, 
the  laws  of  its  action,  and  its  effects  upon  machines. 

In  investigating  the  mathematical  principles  of  Mechanics,  we 
first  proceed  on  the  supposition  that  the  forces  in  question  act  with- 
out any  impediments ;  that  the  surfaces  which  move  in  contact  are 
perfectly  polished  and  suffer  no  friction ;  that  axes  and  pivots  are 
mathematical  lines  and  points ;  that  ropes  are  perfectly  flexible ; 
and,  in  short,  that  the  power  is  transmitted  through  the  machine  to 
the  working  point  without  sustaining  the  least  loss  or  diminution. 
Great  simplicity  is  attained  by  first  bringing  the  subject  to  this  ideal 
standard  of  perfection,  and  afterwards  making  suitable  allowances 
for  all  those  causes  which  operate  in  any  given  case  to  prevent  the 
perfect  action  of  a  machine. 

218.  Surfaces  meet  with  a  certain  degree  of  resistance  in  moving 
on  each  other,  in  consequence  of  the  mutual  cohesion  of  the  parts, 
a  principle  which  has  the  greater  influence  in  any  given  case,  in  pro- 
portion as  the  surfaces  are  smooth.     But  a  much  greater  resistance 


108  MECHANICS. 

arises  from  the  asperities  which  the  surfaces  of  all  bodies  have, 
though  in  very  different  degrees,  according  to  their  different  degrees 
of  smoothness.  An  extreme  case  is  that  of  two  brushes  moving  on 
each  other,  the  hairs  of  which  become  interlaced,  (especially  when 
the  brushes  are  pressed  together,)  and  oppose  a  great  resistance. 
Even  bodies  apparently  very  smooth,  as  polished  metals,  exhibit  un- 
der the  microscope  numerous  inequalities.  Under  the  solar  micro- 
scope, the  finest  needle  exhibits  a  surface  as  rough  as  the  coarest 
iron  tools  do  when  viewed  by  the  naked  eye.  To  these  inequalities 
of  surface,  is  principally  ascribed  the  friction  of  bodies,  when  closely 
in  contact ;  the  prominent  parts  interlock  with  one  another,  or  meet, 
and  must  be  broken  down  before  the  surfaces  can  move.  Hence, 
friction  is  diminished  by  processes  which  level  these  inequalities, 
either  by  polishing  the  surface,  or  by  smearing  it  with  some  lubri- 
cating substance  which  fills  up  the  cavities. 

219.  Forces  of  this  nature,  which' act  by  the  resistance  they  oc- 
casion to  motion  are  called  passive  forces.  They  produce  very  dif- 
ferent effects  in  machines  when  in  a  state  of  equilibrium,  and  in  a 
state  of  motion.  In  the  one  case  they  assist  the  power  ;  in  the  other 
case  they  oppose  it.  Thus,  a  weight  placed  on  an  inclined  plane, 
will  require  a  less  power  to  support  it  in  consequence  of  the  friction 
of  the  plane;  and  a  weight  suspended  by  a  rope  passing  over  a  pulley 
will  require  a  less  weight  to  balance  it,  on  account  of  the  friction  of  the 
axle.  But  the  same  passive  forces  operate  in  just  the  contrary  way 
when  a  machine  is  to  be  put  in  motion  ;  for  then  a  power  must  be 
applied,  which  is  sufficient  not  only  to  overcome  the  weight  itself  but 
also  the  amount  of  all  the  resistances.  For  example,  in  order  to 
draw  a  load  up  an  inclined  plane,  we  have  to  overcome  not  only  the 
force  of  gravity  by  which  the  load  endeavors  to  descend  down  the 
plane,  but  also  the  amount  of  the  friction  and  all  the  other  resistances 
which  impede  its  motion,  although  the  load  would  be  kept  from  de- 
scending, that  is,  in  a  state  of  equilibrium  by  a  less  force  in  conse- 
quence of  these  resistances.  The  principle  is  most  strikingly  ob- 
served in  the  wedge,  where  the  difficulty  of  making  the  wedge  ad- 
vance, is  greatly  increased  by  friction,  but  the  same  cause  operates 
to  prevent  it  from  recoiling. 


FRICTION.  109 

220.  The  forms  under  which  this  sort  of  resistance  presents  itself, 
are  chiefly  of  two  kinds,  namely,  that  of  bodies  sliding,  and  of 
bodies  rolling  on  each  other.     To  the  former  of  these  let  us  first 
attend.     Experiments  on  the  friction  of  sliding  bodies  may  be  made, 
either  by  placing  them  on  a  table,   and  observing  the  weights  which 
they  respectively  require  to  drag  them  along  the  table,  or  by  placing 
them   on  an  inclined  plane,   and  observing  at  what  angle  the   plane 
must  be  elevated  in  order  that  the  body  may  begin  to  slide.     In  the 
former  case,  the  table  is  prepared   by  attaching  a  vertical  pulley  to 
one  edge,  over  which  a  string  is  passed,  one  end  being  connected  to 
the  body  in   question,   and  the  other  end  to  a   pan,  like  that  of  a 
balance,  for  containing  weights.     From  this  simple  arrangement,  a 
great  variety  of  particulars  may  be  ascertained  respecting  the  friction 
of  sliding  surfaces.     A  body  shaped  like  a  brick,  wiih  a  broader  and 
a  narrower  side,  may  be  tried  on  each  of  its  sides  separately,  and  thus 
it  may  be  seen  whether,  in  a  given  weight,  the  extent  of  surface  of 
contact  makes  any  difference ;  the  body  may  be  loaded  with  differ- 
ent weights,  and  hence  may  be  learned   the  influence  of  pressure 
upon  friction ;  the  body  may  be  tried  as  soon  as  it  is  laid  on  the  ta- 
ble,  and  after  remaining  on  it  for*a  longer  or  shorter  time,  in  order 
to  learn  whether  this  circumstance  alters  the  friction ;  different  kinds 
of  bodies  may  be  tried,   and  the  influence  of  different  materials  as- 
certained ;  and  finally  by  dragging  the  body  off  the  table  with  differ- 
ent degrees  of  velocity,  the  relation  of  friction  to  velocity  may  be 
investigated. 

221.  From  experiments  like  the  foregoing,  endlessly  varied,  the 
following  conclusions  have  been  established  : 

(1.)  In  a  given  body  extent  of  surface  makes  no  difference  in  re- 
gard to  friction  ;  a  brick  laid  on  its  edge  meets  with  the  same  resist- 
ance from  this  cause  as  when  laid  on  its  side. 

(2.)  Friction  is  proportioned  to  the  pressure.  If  the  pressure  of 
the  brick  be  doubled  or  trebled  by  laying  weights  upon  it,  the 
amount  of  friction  will  be  increased  in  the  same  ratio. 

(3.)  Friction  is  increased  by  bodies  remaining  for  some  time  in 
contact  with  each  other.  In  some  cases  it  does  not  reach  its  maxi- 
mum under  four  or  five  days.  This  principle  therefore  affects  slow 
motions  much  more  than  such  as  are  rapid.  In  the  mutual  contact 


110  MECHANICS. 

of  metals,  the  friction  attains  its  maximum  almost  instantaneously. 
But  when  metal  rubs  against  wood,  or  one  piece  of  wood  against 
another,  the  friction  is  always  increased  by  resting. 

(4.)  The  friction  is  less  between  surfaces  of  different  kinds  of 
matter,  than  between  those  of  the  same  kind.  Copper  slides  on  cop- 
per, or  brass  on  brass  with  greater  difficulty  than  copper  on  brass ; 
and  it  is  a  general  rule  never  to  let  two  substances  of  the  same  hard- 
ness move  upon  each  other.  To  this  rule,  cast  steel  is  said  to  form 
the  only  exception ;  in  other  cases  pivots  revolve  with  less  resistance 
-on  either  harder  or  softer  substances  than  upon  those  of  the  same 
material  with  themselves.  When  between  the  surfaces  of  wood 
neatly  planed  the  friction  would  be  equal  to  one  half  the  pressure, 
and  when  between  two  metallic  surfaces  it  would  be  equal  to  one 
fourth,  between  the  wood  and  metal  it  would  amount  to  only  one  fifth 
the  pressure. 

(5.)  Friction  is  much  greater  at  the  first  moving  of  a  load,  than 
after  it  is  brought  freely  into  motion.  In  many  instances,  it  is  re- 
duced, when  a  body  has  attained  its  final  velocity,  to  less  than  one 
half  of  what  it  was  at  first.  With  regard  to  different  degrees  of  ve- 
locity in  moving  bodies,  it  is  a  general  principle,  that  the  friction  is 
the  same  for  all  velocities;  that  a  carriage,  for  example,  in  travel- 
ling from  one  place  to  another,  would  encounter  the  same  resistance 
from  friction,  whether  it  performed  the  journey  in  one  hour  or  in  ten. 
The  amount  of  friction,  however,  is  augmented  in  very  slow  motions, 
and  greatly  diminished  in  those  that  are  very  swift.  In  this  instance, 
the  increase  in  the  one  case  and  the  diminution  in  the  other  appears 
to  have  some  relation  to  the  principle,  that  the  friction  of  bodies  is  in- 
creased by  their  remaining  in  contact.  From  some  observations  of 
Professor  Playfair  made  at  the  slide  of  Alpnach,  where  large  fir  trees 
are  carried  with  great  velocity  down  an  inclined  plane  eight  miles  in 
length,  it  would  appear  that,  in  the  case  of  very  great  velocities,  fric- 
tion is  not,  according  to  the  common  doctrine,  either  proportioned 
to  the  pressure  or  independent  of  the  velocity ;  but  that  the  ratio  to 
the  pressure  is  greatly  diminished,  and  the  actual  resistance  is  far 
less  tharT  at  common  velocities.  Thus,  none  but  large  trees  could 
descend  the  plane  at  all ;  and  when  a  tree  broke  into  two  pieces, 
the  larger  part  would  proceed  while  the  smaller  would  stop ;  and  the 
trees  acquired  in  their  descent  a  rapidity  of  motion,  incompatible 


FRICTION.  Ill 

with  the  supposition  that  "  friction  acts  as  a  uniformly  retarding  force," 
which  has  been  considered  as  an  established  principle. 

The  foregoing  considerations  are  in  favor  of  rapid  travelling,  wheth- 
er on  common  roads  or  on  railways,  since  the  amount  of  the  resis- 
tances is  so  much  less  than  in  slow  movements  j  and  accordingly  it 
is  said  that  the  great  speed  given  to  stage  coaches  in  England,  amount- 
ing in  some  instances  to  ten  or  twelve  miles  per  hour,  has  not  been 
attended  with  the  degree  of  exhaustion  to  the  teams  that  would  have 
been  anticipated. 

222.  The  laws  of  friction  in  rolling  bodies  are  ascertained  by 
comparing  the  forces  necessary  to  roll  a  cylinder  upon  a  table  under 
various  circumstances ;  and  by  similar  experiments,  are  found  the 
modes  in  which  friction  takes  place  in  bodies  revolving  on  an  axis* 
The  comparative  loss  of  power  which  takes  place  in  these  three  ca- 
ses is  as  follows : 

Friction  of  the  sliding  body  equal  to  J  the  pressure  or  25  per  cent, 
do.         revolving  do.  15' 

do'         rolling       do.      •  5 

In  the  case  of  hollow  cylinders  revolving  on  an  axis,  the  leverage? 
of  the  wheel  aids  in  overcoming  friction.  Let  fig. 
59,  represent  a  section  of  the  wheel  and  axle.  Let  C 
be  the  center  of  the  axle,  and  let  BE  be  the  hollow 
cylinder  in  the  nave  of  the  wheel'  in  which  the  axle  is 
inserted.  If  B  be  the  part  on  which  the  axle  presses, 
and  the  wheel  turn  in  the  direction  N  DM,  the  fric- 
tion will  act  at  B  in  the  direction  BF,  and  with  the 
leverage  BC.  The  power  acts  against  this  at  D  in  the 
direction  DA,  and  with  the  leverage  DC.  It  is  therefore  evident, 
that  as  DC  is  greater  than  BC,  in  the  same  proportion  does  the  pow- 
er act  with  mechanical  advantage  over  the  friction.  On  this  principle 
an  important  advantage  is  sometimes  gained  in  machines  by  transfer- 
ring the  friction  from  one  point  to  another,  as  from  the  circumference 
to  the  axis  of  a  pulley. 

223.  Friction  Wheels,  a   contrivance  by  which  friction  is  dimin- 
ished in  the  greatest  degree  possible,  owe  their  efficacy  in  part  to  the 
operation  of  the  same  principle.     Here  the  axis  of  a  wheel,  instead 
of  revolving  in  a  hollow  cylinder,  or  instead  of  rubbing  against  a  fixed 


MECHANICS. 

surface,  rests  at  each  of  its  extremities,  on  the  circumference  of  two 
wheels  placed  close  by  the  side  of  each  other,  with  their  circumfer- 
ences intersecting.  The  axis  rests  at  the  point  of  intersection,  and 
as  it  revolves,  the  wheels  revolve  with  it  with  the  same  velocity  and 
thus  all  friction  between  them  and  the  axis  is  prevented,  and  what 
remains  in  the  machine  in  consequence  of  the  weight  of  the  wheels 
themselves  is  transferred  to  their  axles,  and  therefore  is  diminished^ 
in  the  ratio  of  the  diameter  of  one  of  the  wheels  to  that  of  its  axis. 
This  combination  may  be  repeated  by  several  pairs  of  friction  wheels. 
Eight  wheels  would  contract  the  friction  to  the  thousandth  part. 

224.  Other  more  common  methods  of  diminishing  friction   are, 
by  rendering  the  surfaces  smooth,   by  using  rollers,  and  by  lubrica- 
ting the  parts  in  contact.     The  amount  rof  friction  in  the  several  me- 
chanical powers  is  very  different.     In  the  lever  it  is  very  small,  es- 
pecially when  the  turning  edge  is  of  hardened  steel  and  shaped  like 
a  knife  or  prism,   and  turns  upon  a  hard  and  smooth  basis.     The 
Wheel  and  Axle  acting  upon  the  same  principle  as  the  lever,  occa- 
sions but  little  friction.     The  stiffness  of  the  cordage,  however,  and 
the  friction  of  the  gudgeons  of  the  axis  have  an  effect  in  most  cases 
equal  to  about  8  or   10  per  cent,  of  the   entire  resistance.     The 
Pulley  is  attended  with  great  loss  from  this  source.     It  is  rarely  less 
than  20  per  cent  and  often  exceeds  60.     The  Inclined  Plane  in- 
volves but  little  friction  when  bodies  simply  roll  on  it ;  but  when 
heavy  bodies  rest  on  axes,  as  in  wheel  carriages,  the  resistance  from 
friction  takes  place  jn  the  same  manner  as  upon  plane  surfaces.     The 
transportation  on  inclined  planes,  as  railways,  is  usually  by  means  of 
wheels,  since  the  resistance  to  sliding  movements  is  too  great  to  per- 
mit the  use  of  them.     The   Screw  is  attended  with  a  great  deal  of 
friction.     Those  with  sharp  threads  have  more  than  those  with  square 
threads  and  the  endless  screw  has  most  of  all.     In  both  the  Screw 
and  the  Wedge,  the  friction  evidently  exceeds  the  resistance ;  other- 
wise they  would  not  retain  their  position. 

225.  Friction  is  not,  therefore,  in  all  cases  to  be  considered   as 
unfavorable  to  the  operation  of  machinery.     It  is,  in  many  instances, 
a  highly  useful  force.     Many  structures,  as  those  of  Brick  and  stone, 
owe  no  small  part  of  their  stability  to  the  roughness  of  the  materials 


FRICTION.  ,  113 

of  which  they  are  composed  ;  without  this  resistance,  the  screw  and 
the  wedge  would  lose  their  efficacy,  and  the  wheels  could  not  advance, 
nor  could  animals  walk  on  the  ground  ;  and  nails  would  lose  their 
power  of  binding  separate  parts  together.  The  art  of  polishing  sur- 
faces depends  on  the  same  cause,  and  the  edges  of  most  cutting  in- 
struments are  saws,  the  teeth  of  which  are  more  or  less  fine,  and  act 
on  a  similar  principle.  Even  in  certain  rotary  motions,  friction 
becomes  a  moving  force  and  urges  a  body  in  particular  directions 
contrary  to  the  force  of  gravity. 


15 

"••-.•      •«•• 


1J4 


PART    II. HYDROSTATICS. 

CHAPTER  I. 

OF  FLUIDS  AT  REST. 

226.  THE  principles  of  Mechanics  demonstrated  and  explained 
in  the  foregoing  pages,  are  universal  in  their  application,   extending 
alike  to  all  bodies,  whether  solid  or  fluid.     But  in  addition  to  those 
properties  which  fluids  have  in  common  with  solids,  and  which  bring 
them  under  the  general  laws  of  Mechanics,  they  have  also  proper- 
ties peculiar  to  themselves,  which  give  rise  to  a  distinct  class  of  me- 
chanical principles,  not  applicable  to  solid  bodies.     These  are  em- 
braced  under  the  heads  of  HYDROSTATICS   and  PNEUMATICS,  the 
former  division  comprising  the  doctrine  of  liquids,  and  the  latter  that 
pf  aeriform  bodies  or  gases. 

227.  A  FLUID  is  a  body  whose  particles  move  easily  among  them- 
selves,  and  yield  to  the  least  force  impressed ;  and  which,  when  thai 
force  is  removed,  recovers  its  previous  state. 

Since  water,  wind,  and  steam,  are  the  only  fluids  that  are  usually 
employed  as  mechanical  agents,  the  doctrines  of  Hydrostatics  and 
Pneumatics,  have  regard  chiefly  to  them  ;  but  the  principles  estab- 
lished respecting  these,  are  applicable  also  to  all  analogous  bodies. 

It  has  been  usual  to  denominate  liquids  and  gases  respectively 
elastic  and  non-elastic  fluids,  on  the  supposition  that  water  and  other 
liquids  are  nearly  or  quite  incompressible.  An  experiment  perform- 
ed by  the  Florentine  academicians,  as  long  ago  as  1650,  seemed 
to  prove  that  water  is  wholly  incompressible.  They  filled  a  hollow 
ball  of  gold  with  water,  and  subjected  it  to  a  strong  pressure.  The 
water,  nof  yielding  to  the  compression,  oozed  through  the  pores  of 
the  gold.  Considering  the  great  density  and  compactness  of  this 
metal,  the  experiment  was  for  a  long  time  held  as  proving  decisively 
that  water  is  wholly  incompressible.  Although  this  experiment  shows 


FLUIDS    AT    RfcST.  115 

that  water  is  compressed  with  great  difficulty,  yet  later  experiments 
have  proved,  that  it  is  still  capable  of  compression.  The  most  decn 
sive  evidence  of  this  point  has  heen  recently  afforded  by  the  expert 
ments  of  Mr.  Perkins.  It  had  been  previously  ascertained  that  by  a 
pressure  equivalent  to  that  of  the  atmosphere,  or  about  fifteen  pounds 
to  the  square  inch,  water  is  compressed  about  one  part  in  twenty  two 
thousand,  Mr.  Perkins  by  methods  to  be  described  hereafter,  ap- 
plied successive  degrees  of  pressure  up  to  that  of  two  thousand  at- 
mospheres, and  found  the  contraction  of  volume  to  increase  nearly 
in  the  ratio  of  the  compressing  force. 

228.  HYDROSTATICS  is  that  branch  of  N'atural  Philosophy  which 
treats  of  the  mechanical  properties  and  agencies  of  LIQUIDS* 

229.  Fluids  at  rest  press  equally  in  all  directions* 

A  point  in  a  mass  of  flu-id,  taken  at  any  depth,  exerts  and  sustains 
the  same  pressure  in  all  directions,  upwards,  downwards,  or  lat- 
erally. This  is  the  most  remarkable  property  of  fluids,  and  is  what 
particularly  distinguishes  them  from  solids,  which  press  only  down- 
wards, or  in  the  direction  of  gravity.  This  property  naturally  results 
from  the  freedom  of  motion  that  subsists  between  the  particles  of 
fluids ;  for  if,  when  a  fluid  is  at  rest,  the  pressure  on  any  given  por- 
tion were  not  equal  in  all  directions,  that  portion  would  move  in  the 
direction  in  which  the  resistance  was  least.  But  by  the  supposition 
it  does  not  move  :  therefore  it  is  kept  at  rest  by  equal  and  contrary 
forces  acting  on  all  sides.  But  the  most  satisfactory  evidence  of  this 
truth  is  obtained  from  experiment.  On  opening  an  orifice  in  the 
side  of  a  vessel  of  water,  and  estimating  the  force  with  which  the 
water  issues,  it  is  found  to  be  £qual  to  the  weight  of  the  incumbent 
fluid ;  and  the  upward  pressure  of  water  at  a  certain  depth  is  found 
to  sustain  the  heaviest  bodies  when  exposed  to  its  action  alone,  the 
column  above  the  bodies,  and  of  course  the  downward  pressure,  be- 
ing removed, 

230.  A  given  pressure  or  blow  impressed  on  any  portion  of  a  mass 
of  water  confined  in  a  vessel,  is  distributed  equally  through  all  part? 
of  the  mass. 


116 


HYDROSTATICS. 


A  given  pressure,  as  that  made  by  a  plug  forced  inwards  upon  a 
square  inch  of  the  surface  of  a  fluid  confined  in  a  vessel,  is  suddenly 
communicated  to  every  square  inch  of  the  vessel's  surface,  however 
large,  and  to  every  inch  of  the  surface  of  any  body  immersed  in  it. 
Thus,  if  I  attempt  to  force  a  cork  into  a  vessel  full  of  water,  the 
pressure  will  be  felt  not  merely  by  the  portion  of  the  water  directly 
in  the  range  of  the  cork,  but  by  all  parts  of  the  mass  alike  ;  and  the 
liability  of  the  bottle  to  break,  supposing  it  to  be  of  uniform  strength 
throughout,  will  be  as  great  in  one  place  as  another,  and  a  bottle  will 
break  at  the  point  where  it  happens  to  be  weakest,  however  that  point 
may  be  situated  relatively  to  the  place  where  the  cork  is  applied  ;  and 
the  effect  will  be  the  same  whether  the  stopper  be  inserted  at  the  top, 
the  bottom,  or  the  side  of  the  vessel. 

231.  It  is  this  principle  which  operates  with  such  astonishing  effect 
in  the  Hydrostatic  Press,  by  means  of  which  a  single  man  can  exert 
a  force  equal  at  least  to  25000  Ibs.  and  adequate  to  crush  the  hard- 
est substances,  or  cut  in  two  the  largest  bars  of  iron.  Its  construc- 
tion is  as  follows.  Fig.  60  represents  a  press  made  of  the  strongest 
timbers,  the  foundation  of  which  is  commonly  laid  in  solid  masonry. 
AB  is  a  small  cylinder  in  which  moves 
the  piston  of  a  forcing  pump,  and  CD  is 
a  large  cylinder  in  which  also  moves  a 
piston,  having  the  upper  end  of  its  rod 
pressing  against  a  movable  plank  E,  be- 
tween which  and  the  large  beam  above 
is  placed  the  substance  to  be  subjected 
to  pressure,  as  for  example  a  pile  of  new 
bound  books.  By  the  action  of  the  pump 
hancfle,  water  is  raised  into  ihe'smalltyl- 
inder,  and,  on  depressing  the  piston,  it  is  forced  through  a  valve  at  B 
into  the  larger  cylinder  and  raises  the  piston  D,  which  expends  its 
whole  force  on  the  bodies  confined  at  E.  Now  since,  whatever 
force  is  applied  to  any  one  portion  of  the  fluid,  extends  alike  to  every 
part,  therefore  the  force  which  is  exerted  by  the  pump  upon  the 
smaller  column,  is  transmitted  unimpaired  to  every  inch  of  the 
larger  column,  and  tends  to  raise  the  movable  plank  E  with  a 
force  as  much  greater,  in  the  aggregate,  than  that  impressed  upon 


FLUIDS    AT    REST.  117 

the  surface  of  the  smaller,  as  this  surface  is  smaller  than  that  of  the 
larger  column  ;  or  (which  is  the  same  thing)  as  the  number  of  square 
inches  in  the  end  of  the  piston  B  is  less  than  that  of  the  piston  D. 
The  power  of  such  a  machine  is  enormously  great ;  for,  supposing 
the  hand  to  be  applied  at  the  end  of  the  handle,  with  a  force  of  only 
ten  pounds,  and  that  this  handle  or  lever  is  so  constructed  as  to  mul- 
tiply that  force  but  five  times,  the  force  with  which  the  smaller  pis- 
ton will  descend  will  be  equal  to  50  Ibs. ;  and  let  us  suppose  that  the 
head  of  the  larger  piston  contains  the  smaller  50  times,  then  the  force 
exerted  to  raise  the  press  board,  will  equal  2500  Ibs.  A  man  can 
indeed  easily  exert  ten  times  the  force  supposed,  ^and  can  therefore 
exert  a  force  upon  the  substance  under  pressure,  equal  to  25000  Ibs. 

232.  The  rationale  of  the  principle  of  the  Hydrostatic  Press,  will 
be  best  understood  by  recurring  to  the  doctrine  of  Virtual  Velocities. 
It  will  be.  recollected  that  opposite  forces  are  in  equilibrium  when 
their  momenta  are  equal ;  that  a  small  power  may  be  made  to"  bal- 
ance a  great  weight,  by  making  it  move,  in  a  given  time,  over  a 'space 
as  much  greater  than  the  larger  does,  as  its  weight  is  smaller ;  and 
that  it  may  be  made  to  overcome  that  resistance  or  weight,  and  give 
motion  to  it,  if  its  velocity  is  greater  than  that  of  the  latter  in  a  still 
higher  ratio.     Now  to  apply  these  principles  to  the  case  before  us, 
it  is  evident  that  any  quantity  of  water  forced  out  of  the  smaller  into 
the  larger  cylinder,  must  rise  in  the  latter  as  much  slower  as  the  area 
of  the  horizontal  section  is  larger.     If,  for  example,  the  capacity  of 
the  larger  cylinder  were  ten  times  that  of  the  smaller,  then  a  quan- 
tity of  water  one  inch  in  height,  transferred  from  the  smaller  to  the 
greater  cylinder,   would  occupy  only  the  height  of  one  tenth  of  an 
inch,  and  consequently  the  depression  of  the  small  piston  one  inch 
would  raise  the  large  one  only  the  tenth  of  an  inch.     This  case, 
therefore,  resolves  itself  into  that  general   principle,   according  to 
which  a  vast  force  is  exerted  through  a  short  distance,  by  moving  a 
small  force  through  a  distance  much  greater. 

233.  The  surface  of  a  fluid  at  rest  is  horizontal. 

The  evidence  of  the  truth  of  this  proposition  is  threefold.     First, 
this  result  is  a  natural  consequence  of  the  mobility  of  fluids,  since,  if 


118  HYDROSTATICS. 

any  portion  is  raised  above  the  rest,  having  nothing  to  support  it,  and 
being  acted  on  by  gravity,  it  must  descend  in  the  same  manner  as  a 
body  placed  on  a  perfectly  smooth  inclined  plane.  Secondly,  when- 
ever a  body  is  free  to  move,  its  center  of  gravity  will  descend  as  low 
as  possible.  When,  therefore,  any  portion  of  a  fluid  is  raised  above 
the  general  level,  the  center  of  gravity  of  the  mass  is  raised,  and  it 
must  return  before  the  fluid  can  be  at  rest.  Thirdly,  experience 
shows  that  the  proposition  is  true,  since  fluids,  when  free  to  move, 
always  settle  themselves  with  their  surfaces  parallel  to  tbe  horizon. 
It  must  be  understood,  however,  that  the  surface  of  large  bodies  of 
water  is  not,  strictly  speaking,  a  horizontal  level,  but  is  a  portion  of 
the  convex  surface  of  the  earth ;  for  since  the  center  of  gravity  of 
every  portion  of  the  fluid  will  descend  as  low  as  possible,  the  whole 
will  dispose  itself  around  the  center  of  attraction  so  as  to  form  a  por- 
tion of  the  earth's  surface.  For  small  distances  the  curvature  is  so 
slight  that  it  may  be  neglected,  not  amounting  to  one  second  of  a  de- 
gree for  100  feet;  and  for  the  distance  of  a  mile,  the  deviation  from 
a  straight  line,  drawn  in  the  direction  of  a  tangent,  is  not  more  than 
8  inches. 

234.  A  practical  application  of  this  principle  is  made  in  the  art  of 
levelling.     A  level  is  sometimes  made  by  merely  cutting  a  groove  or 
channel  in  a  flat  piece  of  board  and  filling  it  with  water.     When  the 
board  is  brought  into  such  a  situation  that  the  water  in  the  groove  re- 
mains stationary,  the  position  is  horizontal.     But  the  spirit  level  is 
the  instrument  more  commonly  employed  for  this  purpose.     This 
consists  of  a  small  cylindrical  tube  of  glass,  from  two  to  six  inches 
long,  filled  with  spirits  of  wine  or  ether,  except  a  small  space  which 
is  occupied  by  a  movable  bubble  of  air.    When  such  a  tube  is  placed 
horizontally,  the  bubble  of  air  will  remain  stationary  in  the  center  of 
the-  tube,  at  a  fixed  mark  ;  but  whenever  the  tube  is  inclined,  in  the 
least  degree,  the  bubble  will  ascend  towards  the  elevated  end.    Spirit 
levels  are  much  used  for  adjusting  astronomical,  surveying,  and  other 
delicate  instruments. 

235.  The  pressure  upon  any  particle  of  a  fluid  of  uniform  densi- 
ty, is  proportioned  to  its  depth  below  the  surface. 


FLUIDS    AT    REST. 


119 


Thus  in  Fig.  61,  the  pressure  exerted 
by  the  fluid  at  different  depths  as  x  and 
y  is  found  to  be  exactly  proportioned  to 
their  depth  below  the  surface,  so  that  if 
y  be  twice  as  deep  as  a?,  a  body  at  y 
would  sustain  twice  as  much  pressure  as 
at  x.  But  since  the  inclined  column 
AC  etc,  is  of  the  same  perpendicular 
height  as  the  erect  column  ABCD,  both 
exert  the  same  pressure  on  the  base  AC. 


(i) 


A    C 


236.  According  to  Art.  229,  the  lateral  is  equal  to  the  downward 
pressure ;  and  consequently  on  this  principle  may  easily  be  estimated 
the  amount  of  pressure  on  the  sides  of  any  column  of  water,  or  on 
the  banks  of  rivers,  canals,  &c.  At  the  depth  of  8  feet,  the  press- 
ure on  a  square  foot  is  equal  to  the  weight  of  a  column  of  water, 
whose  base  is  1  foot  and  depth  8  feet,  and  consequently  its  solid  con- 
tents 8  cubic  feet;  and  since  1  cubic  foot  of  water  weighs  1000 
ounces  or  62jlbs.  therefore  the  weight  of  the  column  =  8x62j= 
500  Ibs.  Hence  the  pressure  on  a  square  foot,  at  different  depths, 
will  be  as  in  the  following  table. 


Depth  in  feet 

8    . 

Pressure  on  a  square  foot. 

•./•>.  .,     500  Ibs. 

Depth  in  feet.    Pressure  on  a  square  foot, 
56    ....  3500  Ibs. 

16    . 

..  ;  .     .  1000 

64    ....  4000 

24    . 

:  ;-;.  •••.     .  1500 

72    ....  4500 

32    . 

.     .     .  2000 

80    ....  5000 

40    . 

.     .     .  2500 

38    ....  5500 

48    . 

..  '  .     .  3000 

96    ....  6000 

1  mile  or  5280  feet, 
5    " 

.     .     .     330,000  Ibs. 
1.650.000 

Hence  it  appears  that  at  the  moderate  depth  of  64  feet,  the  pressure 
of  a  column  of  water  on  the  bottom  or  sides  of  the  containing  pipe, 
becomes  4000  Ibs.  to  the  square  foot ;  and  the  pressure  on  the  bot- 
tom of  the  sea,  where  it  is  one  mile  in  depth,  is  330,000  Ibs.  to  the 
square  foot,  and  where  it  is  five  miles  deep,  that  pressure  is  no  less 
than  1,650,000  Ibs.*  From  these  considerations  we  may  readily 


*  Allowance  must  always  be  made  for  the  saltness  of  the  sea,  salt 
water  being  heavier  than  fresh. 


120  HYDROSTATICS. 

apprehend  the  cause  of  the  great  difficulty  experienced  in  confining 
a  high  column  of  water;  and  hence  also  may  be  inferred  the  immense 
pressure  that  is  exerted  on  the  bottom  of  the  sea. 

237.  Indications  of  this  vast  pressure  in  deep  waters,  are  mani- 
fested by  several  interesting  facts.     It  has  long  been  known  to  mari- 
ners, that  if  a  common  square  bottle  be  let  down  into  the  sea,  its  sides 
are  crushed  inwards  before  it  has  reached  the  depth  of  ten  fathoms. 
If  a  stronger  bottle,  (a  common  junk  bottle,  for  example,)  be  filled 
with  water,  corked  close,  and  let  down  to  a  certain  depth,  either  the 
cork  will  be  forced  inwards,  or  if  that  is  secured  in  its  place,  the  salt 
water  will  make  its  Way  into  the  bottle  in  spite  of  it,  either  by  com- 
pressing the  cork  or  by  forcing  in  water  through  it.     It  was  by  sink- 
ing an  apparatus  to  the  depth  of  500  fathoms,  that  Mr.  Perkins  first 
proved  the  compressibility  of  water,  as  mentioned  in  Art.  227.     The 
apparatus  consisted  of  a  hollow  brass  cylinder,   resembling  a  small 
cannon,  and  furnished   with  a  stopper  so  contrived  as  to  indicate, 
when  the   apparatus  was  drawn  up,  how  far  it  had  been  driven  in 
while  at  the  lowest  depth.     The  same  experiments  were  afterwards 
repeated  on  shore,  a  pressure  being  applied  to  the  plug,  by  means  of 
the  hydrostatic  press,  equivalent  to  2000  atmospheres. 

Tire-increase  of  pressure  in  proportion  to  the  depth  of  the  fluid, 
renders  it  necessary  to  make  the  sides  of  pipes  or  masonry,  in  which 
fluids  are  to  be  contained,  stronger  the  deeper  they  go.  The  same 
remark  applies  to  dams,  flood-gates,  and  banks. 

238.  'At  the  depth  of  1000  fathoms,  the  compression  of  water  is 
one  twentieth  of  its  bulk,  and  its  specific  gravity  is  increased  in  the 
same  ratio ;  so  that  bodies  which  sink  near  the  surface  of  the  sea, 
may  float  at  a  certain  depth  before  they  reach  the  bottom.     On  the 
other  hand,  a  porous  body,  that  is  light  enough  to  float  near  the  sur- 
face, will  have  so  much  water  forced  into  its  pores,  when  it  is  sunk 
to  a  great  depth,  as  never  to  rise.     This  is  the  case  with  ships  that 
are  wrecked  in  deep  water ;  the  parts  of  the  wreck  do  not  rise  to 
the  surface,  as  they  do  in  shallow  water. 

239.  When  a  portion,  as  a  square  foot,  of  the  lateral  surface  of  a 
column  of  water,  is  taken,  all  parts  of  it  are  not  equally  distant  from 
the  surface  of  the  fluid ;  and,   in  this  case,   the  average  depth,  or 


FLUIDS    AT    REST. 


121 


(which  is  the  same  thing)  the  depth  of  the  center  of  gravity,  is  to  be 
understood  according  to  the  following  proposition,  which  applies  to 
every  sort  of  surface,  however  inclined  to  the  horizon. 

The  pressure  of  a  fluid  against  any  surface,  in  a  direction  per- 
pendicular to  it,  varies  as  the  area  of  the  surface  multiplied  into  the 
depth  of  its  center  of  gravity  below  the  surf  ace  of  the  fluid. 

Hence,  the  pressure  on  the  side  of  a  cubical  vessel,  filled  with 
fluid,  is  one  half  the  pressure  against  the  bottom  ;  and  the  whole 
pressure  against  the  sides  and  bottom,  is  equal  to  three  times  the 
weight  of  the  fluid  in  the  vessel. 

240.  Fluids  rise  to  the  same  level  in  the  opposite  arms  of  a  re- 
curved tube. 

Let  ABC,  (Fig.  62.)  be  a  recurved  tube  :  if  Fig.  62. 
water  be  poured  into  one  arm  of  the  tube,  it  will 
rise  to  the  same  height  in  the  other  arm.  For,  by 
Art.  235,  the  pressure  upon  the  lowest  part  at  B, 
in  opposite  directions,  is  proportioned  to  its  depth 
below  the  surface  of  the  fluid/  Therefore,  these  A 
depths  must  be  equal,  that  is,  the  heights  of  the 
two  columns  must  be  equal,  in  order  that  the  fluid 
at  B  may  be  at  rest ;  and  unless  this  part  is  at  rest, 
the  other  parts  of  the  column  cannot  be  at  rest. 
Moreover,  since  the  equilibrium  depends  on  nothing 
else  than  the  heights  of  the  respective  columns, 
therefore,  the  opposite  columns  may  differ  to  any 
degree  in  quantity,  shape,  or  inclination  to  the  ho- 
rizon. Thus,  if  vessels  and  tubes  very  diverse  in  shape  and  capaci- 
ty, as  in  Fig.  63,  be  connected  with  a  common  reservoir,  and  water 

Fig.  63. 


122  HYDROSTATICS. 

be  poured  into  any  one  of  them,  it  will  rise  to  the  same  level  in 
them  all. 

The  reason  of  this  fact  will  be  farther  understood  from  the  ap- 
plication of  the  principle  of  Virtual  Velocities,  (Art.  179.) ;  for  it 
will  be  seen  that  the  velocity  of  the  columns,  when  in  motion,  will 
be  as  much  greater  in  the  smaller  than  in  the  larger  columns,  as  the 
quantity  of  matter  is  less ;  and  hence  the  opposite  momenta  will  be 
constantly  equal. 

241.  Hence,   water  conveyed  in  aqueducts  or  running  in  natural 
channels,  will  rise  just  as  high  as  its  source.     Between  the  place 
where  the  water  of  an  aqueduct  is  delivered  and  the  spring,  the 
ground  may  rise  into  hills  and  descend  into  valleys,  and  the  pipes 
which  convey  the  water  may  follow  all  the  undulations  of  the  coun- 
try, and  the  water  will   run  freely,  provided  no  pipe  is  laid  higher 
than  the  level  of  the  spring.     Waters  running  in  natural  channels  in 
the  earth  are  governed  by  the  same  law. 

242.  The  acqueducts  constructed  by  the  ancient  Romans,  were 
among  the  most  costly  ornaments  of  their  arts.     Several  of  them 
were  from  thirty  to  one  hundred  miles  in  length,  and  consisted  of  vast 
covered  canals,  built  of  stone.     They  were  carried  over  valleys  and 
level  tracts  of  country  upon  arcades,   which  were  sometimes  of  stu- 
pendous height  and  solidity.     From  the  fact  that  the  ancients  built 
acqueducts  with  so  much  labor,  raising  them  to  a  great  height  in  cross- 
ing valleys,  instead  of  availing  themselves  of  the  principle  under  con- 
sideration, some  have  supposed  that  they  were  unacquainted  with  this 
principle.     It  appears  nevertheless  that  they  were  acquainted  with  it 
and  even  understood  the  use  of  pipes  in  conveying  water;  but  prob- 
ably the  expense  of  pipes,  and  the  difficulty  of  making  them  strong 
enough  to  resist  the  pressure  when  laid  at  a  considerable  depth  below 
the  source,  prevented  their  general  use. 

243.  The  pressure  upon  the  horizontal  base  of  any  vessel  contain- 
ing a  fluid  is  equal  to  the  weight  of  a  column  of  the  fluid,  found  by 
multiplying'lhe  area  of  the  base  into  the  perpendicular  height  of  the 
column,  whatever  be  the  shape  of  the  vessel. 

This  follows  from  Art.  239,  since,  here  the  distance  of  the  center 
of  gravity  from  the  surface  of  the  fluid,  is  the  same  as  the  perpen- 


FLUIDS  AT  REST, 


123 


Fig.  64. 


dicular  height  of  the  column.  With  a  given  base  and  height,  there- 
fore, the  pressure  is  the  same  whether  the  vessel  is  larger  or  smaller 
above,  whether  its  figure  is  regular  or  irregular,  whether  it  rises  to 
the  given  height  in  a  broad  open  funnel,  or  is  carried  up  in  a  slender 
tube.  Hence,  any  quantity  of  water,  however  small,  may  be  made 
to  balance  any  quantity,  however  great.  This  is  called  the  hydro- 
static paradox.  The  experiment  is  usually  performed  by  means  of 
a  water  bellows,  as  is  represented  in  Fig.  64.  When  the  pipe  AD 
is  filled  with  water  the  pressure  upon  the  sur- 
face of  the  bellows,  and  consequently  the  force 
with  which  it  raises  the  weights  laid  on  it,  will 
be  equal  to  the  weight  of  a  cylinder  of  water, 
whose  base  is  the  surface  of  the  bellows  and 
height  that  of  the  column  AD.  Therefore,  by 
making  the  tube  small  and  the  bellows  large, 
the  power  of  a  given  quantity  of  water,  how- 
ever small,  may  be  increased  indefinitely.  The 
pressure  of  the  column  of  water  in  this  case 
corresponds  to  the  force  applied  by  the  piston 
in  the  Hydrostatic  Press,  (Art.  231.)  .and  the 
explanation  according  to  the  principle  of  vir- 
tual velocities,  is  the  same  in  both  cases. 

244.  The  principle  of  the  Hydrostatic  Paradox,  is  sometimes  ex- 
emplified in  pouring  liquids  into  casks,  throngh  long  tubes  inserted  in 
the  bung  holes.  As  soon  as  the  cask  is  full,  and  the  water  rises  in 
the  pipe  to  a  certain  height,  the  cask  bursts  with  violence.  The 
same  cause  is  supposed  sometimes  to  produce  great  effects  in  nature, 
such  as  splitting  rocks,  heaving  up  mountains,  and  other  effects  re- 
sembling earthquakes.  For,  suppose  that  in  the  interior  of  a  moun- 
tain there  were  an  empty  space  ten  yards  square,  and  only  an  inch 
deep,  in  which  water  had  lodged  so  as  to  fill  it  entirely;  and  suppose 
that  a  crevice  in  the  earth  should  extend  from  this  spot  200  feet 
above,  which  should  also  become  filled  with  water  by  rain  or  other- 
wise :  the  force  exerted  would  be  adequate  to  shake  the  mountain, 
and  perhaps  rend  it  asunder. 

245.  Although  the  weight  of  a  given  quantity  of  water  will  not  be 
altered  by  varying  the  shape  of  the  vessel,  yet  the  pressure  which  it 


124  HYDROSTATICS. 

exerts  on  the  bottom  of  the  vessel  will  be  greater  in  proportion  as 
the  altitude  of  the  mass  is  greater,  and  of  course  greater  in  a  narrow 
vessel  than  in  a  wide  one.  If  it  be  asked  why  the  weight  is  not  in- 
creased as  the  downward  pressure  is  increased,  the  answer  is  that 
the  pressure  in  that  direction  is  exactly  counterbalanced  by  an  equal 
pressure  in  the  opposite  direction. 

Specific  Gravity. 

246.  The  Specific  Gravity  of  a  body,  is  its  weight  compared  with 
the  weight  of  another  body  of  the  same  bulk,  taken  as  a  standard. 

Water  is  the  standard  for  all  solids  and  liquids,  and  common  air 
for  the  gases.  Therefore,  the  specific  gravity  of  a  solid  or  a  liquid 
body  is  the  ratio  of  its  weight  to  the  weight  of  an  equal  volume  of 
water ;  and  the  specific  gravity  of  an  aeriform  body,  is  the  ratio  of  its 
weight  to  the  weight  of  an  equal  volume  of  air.  But  a  ratio  is  ex- 
pressed by  a  vulgar  fraction,  whose  numerator  is  the  antecedent  and 
whose  denominator  is  the  consequent.  If,  therefore,  the  weight  of  a 
body  is  made  the  numerator,  and  the  weight  of  an  equal  volume  of 
water  .the  denominator,  the  value  of  the  fraction,  that  is,  the  quotient, 
will  express  the  specific  gravity  of  the  body.  Hence,  the  weight  of 
a  body  being  given,  and  being  made  the  numerator,  every  process 
for  finding  the  specific  gravity  consists  in  finding  for  the  denominator 
the  weight  of  an  equal  bulk  of  water  or  air.  The  principles  upon 
which  the  methods  of  doing  this  depend,  are  now  to  be  explained. 

247.  A  body  immersed  in  a  fluid,  loses  as  much  weight  as  is  equal 
to  the  weight  of  an  equal  volume  of  the  fluid. 

Let  EF  (Fig.  65.)  be  a  solid  body  im- 
mersed  in  a  vessel  of  water  or  any  fluid, 
and  suppose  it  divided  into  an  indefinite 
number  of  perpendicular  columns,  reach- 
ing to  the  surface  of  the  fluid,  as  mon. 
Now  the  upward  pressure  at  n  is  as  its 
depth,  and  the  downward  pressure  at  o 
as  its  depth ;  therefore  the  upward  pressure  exceeds  the  downward, 
by  the  weight  of  a  column  of  water  equal  to  n  o.  The  same  is  true 


SPECIFIC    GRAVITY.  125 

of  all  the  columns,  however  numerous  they  may  be,  that  can  be 
drawn  parallel  to  n  o;  but  these  columns,  taken  collectively,  make 
up  a  body  of  water  equal  in  bulk  to  the  solid.  Hence,  the  solid  is 
pressed  upwards  more  than  downwards,  by  the  weight  of  a  quantity 
of  water  of  the  same  magnitude,  and  consequently  loses  so  much  of 
its  weight.  Hence,  the  specific  gravity  of  any  solid  body  that  will 
sink  in  water,  is  found  by  the  following 

RULE. — Divide  the  weight  of  the  body  by  its  loss  of  weight  in 
water. 

248.  When  the  body  whose  specific  gravity  is  required  is  lighter 
than  water,  as  a  cork,  for  example,  the  object  is  still  to  find  the  weight 
of  an  equal  bulk  of  water,  since  that  will  constitute  the  denominator, 
or  divisor,  as  before.     To  ascertain  this,  suspend  any  heavy  body,  as 
a  mass  of  lead  or  glass,  in  water  and  find  its  weight.     Attach  to  it 
the  lighter  body.     Now  the  cork  will  not  only  lose  all  its  own  weight 
but  will  diminish  the  weight  of  the  heavy  body;  and  the  weight  of  an 
equal  bulk  of  water  will  be  indicated  by  the  whole  of  what  the  cork 
loses,  namely,  its  own  weight  added  to  the  loss  occasipned  to  the 
other  body.     Whence  we  have  the  following 

RULE. — To  find  the  specific  gravity  of  a  body  lighter  than  wa- 
ter. Divide  its  weight  by  the  sum  of  its  weight  added  to  the  loss  of 
iveight  which  it  occasions  in  a  heavy  body  previously  balanced  in  water. 

249.  A  solid  which  is  soluble  in  water,  as  a  lump  of  salt,  is  pro- 
tected  from  solution  by  smearing  it  with  oil  or  a  thin  coat  of  bees 
wax ;  and  solids  that  are  very  porous  and  would  absorb  water,  and 
thus  increase  their  specific  gravities,  as  certain  kinds  of  wood,  are 
first  covered  with  varnish.     The  specific  gravity  of  solid  substances, 

.which  are  too  minutely  divided  to  be  weighed  in  water  separately,  as 
grains  of  sand  or  shot,  may  be  found  by  weighing  them  in  a  small 
bucket  previously  balanced  in  water. 

250.  The  specific  gravity  of  liquids  may  be  ascertained  by  seve- 
ral different  methods. 

RULE  I. —  Weigh  equal  volumes  of  the  liquid  and  of  water,  and 
divide  the  former  result  by  the  latter. 


126 


HYDROSTATICS. 


Fig.  66. 


RULE  II. — Ascertain  the  loss  of  weight  of  any  solid  body,  first  in 
the  liquid  and  then  in  water,  and  divide  the  former  result  by  the  latter. 

Both  these  rules  obviously  depend  upon  the  same  principles  as 
those  explained  in  Art.  246,  the  weight  of  the  liquid  being  immedi- 
ately compared  with  that  of  an  equal  bulk  of  water;  but  there  is 
another  method,  founded  on  the  following  proposition. 

251.  Two  columns  of  fluids  of  different  specific  gravities,  pressing 
freely  on  each  other  at  their  bases,  balance  one  another  when  their 

heights  are  inversely  as  their  specific  gravities. 

Let  AB  (Fig.  66.)  be  a  recurved  tube,  and  let  the 
height  of  the  column  of  the  fluid  B  be  as  much  great- 
er than  that  of  A,  as  the  fluid  B  is  lighter  than  the 
fluid  A  ;  the  two  columns  will  then  be  in  equilibrio. 

If  the  tube  be  of  uniform  bore  throughout,  then  the 
proposition  is  manifestly  true,  because  the  quantities  of 
matter  pressing  on  each  other  in  opposite  directions 
will  be  equal,  and  will  have  equal  momenta  ;  but  from 
the  peculiar  nature  of  fluids,  (Art.  235.)  the  opposite 
pressures  will  be  the  same,  when  the  heights  of  the 
columns  are  the  same,  whatever  may  be  the  shape  or 
capacity  of  the  tube.  If  we  introduce  mercury  into 
one  arm  of  the  tube  and  water  into  the  other,  the 
graduated  scale  will  indicate  that  the  water  stands  13£ 
times  as  high  as  the  mercury.  Therefore,  the  specific 
gravity  of  mercury  is  13J.  Proof  spirit  will  stand  at 
.923;  sweet  oil  at  .915;  and  their  specific  gravities 
are  the  same,  water  being  1 . 

252,  If  a  body  floats  on  a  fluid,  it  displaces  as  mucJi  of  the  fluid 
as  is  equal  to  its  own  weight. 

If  into  a  vessel  full  of  water  a  floating  body,  as  a  piece  of  wood, 
be  introduced,  the  quantity  of  water  displaced  will  be  found  to  be 
exactly^qual  in  weight  to  the  body.  Or  if  the  vessel  of  water  be 
accurately  balanced  in  a  scale,  and  then  removed  and  the  piece  of 
wood  introduced,  the  vessel  on  restoring  it  to  the  scale,  will -still  re- 
main in  equilibrium,  the  wood  exactly  compensating  for  the  water  it 
displaced. 


SPECIFIC    GRAVITY.  127 

253.  An  accurate  knowledge  of  the  specific  gravities  of  bodies, 
is  of  great  use  for  many  purposes  of  science  and  the  arts,  and  they 
have  therefore  been  determined  with  the  greatest  possible  precision. 
The  heaviest  of  all  known  substances  is  platina,  whose  specific  gravi- 
ty, in  its  state  of  greatest  condensation,  is  22,  water  being  1 ;  and 
the  lightest  of  all  ponderable  bodies  is  hydrogen  gas,  whose  specific 
gravity  is  .073,  common  air  being  1 .  By  calculation,  it  will  be  found 
that  platina  is  about  247,000  times  as  heavy  as  hydrogen,  and  hence 
a  wide  range  is  allowed  to  the  various  bodies  which  lie  between  these 
extremes.  The  metals,  as  a  class,  are  the  heaviest  bodies ;  next  to 
these  come  the  metallic  ores ;  then  the  precious  gems ;  and  finally, 
minerals  in  general,  animal,  liquid  and  vegetable  substances,  in  order, 
according  to  the  following  table. 

Metals,  (pure,)  not  including  the  bases  of  the  alkalies  and  earths, 
from  -     5  to  22 

Gold  19.25         Steel  -     7.84 

Quicksilver  -    13.58         Iron  -     7.78 

Lead  -    11.35         Tin  -         -     7.29 

Silver       -  -    10.47         Zinc  .      7.00 

Copper    -  -     8.90 

Metallic  Ores,  lighter  than  the  pure  metals,  but  usually  above  4.00 
Precious  Gems,  as  the  ruby,  sapphire  and  diamond,  3 — 4 

Minerals,  comprehending  most  stony  bodies,  2 — 3 

Liquids,  from  ether  highly  rectified  to  sulphuric  acid  highly 

concentrated,     -  -    5 — 2 

Acids  in  general,  heavier  than  water. 

Oils,     do.     lighter  ;  but  the  oils  of  cloves  and  cinnamon  are  heav- 
ier than  water;  the  greater  part  lie  between  .9  and  1.     -     .9 — 1 
Milk,  -     1.032 

Alcohol  (perfectly  pure,)       -  -       .797 

Do.     of  commerce,  -       .835 

Proof  Spirit,  -         .       .923 

Wines ;  the  specific  gravity  of  the  lighter  wines,  as  Champagne  and 
Burgundy,  is  a  little  less,  and  of  the  heavier  wines,  as  Malaga,  a 
little  greater,  than  that  of  water. 
Woods,  cork  being  the  lightest  and  lignum  vitas  the  heaviest,  J  to  1 J. 

254.  If  we  balance,  in  a  pair  of  scales,  a  tumbler  filled  with  water 
to  a  certain  mark  near  the  top,  and  then,  turning  out  all  the  water 


128  HYDROSTATICS. 

except  a  small  quantity,  introduce  any  solid  body,  (as  a  tumbler  a 
little  less  than  the  first,)  so  as  to  raise  the  water  on  the  sides  to  the 
same  mark  as  before,  the  equilibrium  will  be  restored.  Here,  the 
space  occupied  by  the  solid  immersed,  is  the  same  with  that  before 
occupied  by  the  water.  On  the  same  principle,  a  ship  is  floated  in 
a  dock  with  a  very  small  quantity  of  water,  and  still  rides  as  freely 
as  on  the  ocean.  By  the  ascent  of  the  water  on  the  sides,  the  up- 
ward pressure  on  the  bottom  is  increased,  on  the  same  principle  as 
in  the  Hydrostatic  Paradox,  (Art.  243.)  Though,  in  this  case,  we 
cannot  say  that  a  quantity  of  water  is  displaced  equal  in  weight  to  the 
solid,  (since  the  whole  of  the  water  originally  in  the  vessel  may  not 
have  been  nearly  sufficient  to  fill  the  space  occupied  by  the  ship,) 
yet  the  effect  is  the  same,  in  regard  to  the  pressure  on  the  water  be- 
low the  ship,  and  of  course  on  the  upward  pressure,  (Art.  229.)  as 
though  the  space  occupied  by  the  ship  below  the  level  of  the  fluid 
on  its  sides,  were  filled  with  water.  On  this  principle,  the  weight  of 
a  loaded  boat  in  the  lock  of  a  canal  is  easily  estimated. 

Boats  are  sometimes  made  of  iron  instead  of  wood,  their  thickness 
being  so  much  less,  that  the  entire  weight  of  the  boat,  is  not  greater 
than  when  made  of  wood. 

255.  The  human  body,  when  the  lungs  are  filled  with  air,  is 
lighter  than  water,   and  but  for  the  difficulty  of  keeping  the  lungs 
constantly  inflated,  it  would  naturally  float.     With  a  moderate  de- 
gree of  skill,  therefore,  swimming  becomes  a  very  easy  process,  es- 
pecially in  salt  water.     When,  however,   a  man  plunges,  as  divers 
sometimes  do,  to  a  great  depth,  the  air  in  the  lungs  becomes  com- 
pressed, and  the  body  does  not  rise  except  by  muscular  effort.     The 
bodies  of  drowned  persons  rise  and  float  after  a  few  days,  in  conse- 
quence of  the  inflation  occasioned  by  putrefaction.     Quadrupeds 
swim  much  more  easily  than  man,  because  the  motion  of  the  limbs 
necessary  to  sustain  themselves,  nearly  coincide  with  their  natural 
motions  in  walking,  while  the  body  maintains  nearly  its  usual  posture. 

256.  Ma  body  is  held  beneath  the  surface  of  a  fluid,  the  force  with 
which  it  will  ascend,  if  it  is  lighter  than  the  fluid,  or  with  wKich  it 
will  descend,  if  it  is  heavier,  is  equal  to  the  difference  between  its  own 
weight  and  the  weight  of  an  equal  quantity  of  the  fluid. 


SPECIFIC    GRAVITY. 

On  the  foregoing  principle,  is  founded  the  construction  of  a  ma- 
chine called  the  Camel,  for  raising  sunken  vessels,  or  for  lifting  ships 
over  sand  banks.  Empty  hogsheads  or  boxes  sunk  by  means  of 
weights  which  are  afterwards  detached,  being  fixed  to  a  sunken  ship, 
may  give  it  so  much  buoyancy  as  to  cause  it  to  float.  Suppose,  for 
example,  a  hundred  empty  hogsheads  were  thus  attached,  what  up- 
ward force  would  they  exert  ? 

The  number  of  gallons  in  a  hogshead,  63,  multiplied  by  231,  the 
number  of  inches  in  a  gallon,  gives  14553  inches ;  which,  divided 
by  1728,  gives  8.4  cubic  feet  in  a  hogshead.  But  a  cubic  foot  of 
water  weighs  62J  pounds.  Therefore,  62.5  X  8.4=525  lbs.=weight 
of  a  hogshead  of  water. 

Now  100  cubic  inches  of  air  weighs  30  J  grains ;  therefore, 
100  :  30J: 114553  :  4438.66=grains  of  air  in  a  hogshead;  or 
(since  437.5  grs.  equal  an  ounce)  the  number  of  ounces  of  air  in  a 
hogshead  is  10,14.  Hence  525  Ibs.- 10,14  oz.  =  534  Ibs.  6  oz. 
nearly,  for  the  upward  force  of  an  empty  hogshead  sunk  in  water ; 
consequently,  the  buoyancy  of  100  hhds.  is  52437.5  pounds,  or  al- 
most 23J  tons. 

A  similar  effect  is  exhibited  in  rivers,  where  the  ice  is  formed 
upon  the  stones  at  their  bottom.  Ice  is  specifically  lighter  than  wa- 
ter, and  therefore  when  it  accumulates  to  a  certain  degree  around 
the  stones,  the  upward  pressure  upon  the  stones  exceeds  their  press- 
ure downwards,  and  they  are  brought  to  the  surface,  having  been 
sometimes  torn  up  with  great  force.  Huge  masses  of  stones  appear 
in  many  cases  to  have  been  floated  by  the  ice  adhering  to  them,  and 
carried  to  a  great  distance  from  the  place  .of  their  formation. 

257.  Rocks  and  stones  being  only  a  little  more  than  twice  as  heavy 
as  water,  of  course  nearly  half  their  weight  is  sustained  while  they 
are  immersed  in  water ;  and  hence  the  increased  weight  which  is 
felt  when  a  large  stone  is  lifted  from  the  bed  of  a  river,  as  soon  as  it 
reaches  the  surface.  Large  masses  of  rocks  are  transported  with1 
far  greater  facility  by  torrents,  on  account  of  their  diminished  weight. 
On  the  same  principle,  the  limbs  feel  very  heavy  on  leaving  a  bath. 
Life  boats  have  a  large  quantity  of  cork  mixed  in  their  structure ; 
or  of  air-tight  vessels  of  thin  copper  or  tin  plate,  so  that,  even  when 

17 


130  HYDROSTATICS. 

the  boats  are  filled  with  water,  a  considerable  part  still  floats  above 
the  surface. 

258.  The  magnitudes  of  bodies  may  frequently  be  most  conven- 
iently and  accurately  estimated  from  the  doctrine  of  specific  gravities. 
Suppose  we  wish  to  ascertain  the  exact  number  of  solid  inches  con- 
tained in  a  stone  of  rude  and  irregular  shape,  we  should  find  great 
difficulty  in  applying  to  it  any  linear  measurements ;  but  if  we  ascer- 
tain its  loss  of  weight  in  water,  we  then  have  the  weight  of  an  equal 
bulk  of  water,  and  since  1000  ounces  contain  1728  cubic  inches, 
we  may  easily  find  how  many  cubic  inches  correspond  to  the  weight 
of  water  of  equal  magnitude  with  the  body  in  question.  For  exam- 
ple, when  we  want  to  find  the  number  of  solid  inches  in  a  chain,  the 
irregularity  of  its  shape  prevents  our  applying  to  it  any  linear  measure ; 
but  if  we  weigh  it  in  water,  and  subtract  this  weight  from  its  weight 
in  air,  the  difference  gives  us  the  weight  of  a,n  equal  bulk  of  water, 
which  we  can  easily  convert  into  solid  inches.  Suppose  the  chain 
loses  2.34  ounces  by  being  weighed  in  water,  then 

1000  oz.  :  1728  in. ::  2.34  oz.  I  4.04  inches. 
That  is,  the  chain  contains  a  little  more  than  four  solid  inches. 


CHAPTER  II. 

OF  LIQUIDS  OR  NON-ELASTIC  FLUIDS  IN  MOTION. 

259.  That  branch  of  Natural  Philosophy  which  treat  of  fluids  in 
motion,  is  usually  denominated  Hydraulics.     It  embraces  the  phe- 
nomena exhibited  by  water  issuing  from  orifices  in  reservoirs — pro- 
jected obliquely  or  perpendicularly — flowing  in  pipes,  canals,  and 
rivers — oscillating  in  waves — or  opposing  a  resistance  to  the  progress 
of  solid  bodies. 

260.  If  a  fluid  runs  through  any  lube,  pipe,  or  canal,  and  keeps 
it  constantly  full,  its  velocity  in  any  part  of  its  course,  will  be  in- 
versely a&4he  area  of  the  section  at  that  part. 

Thus,  in  a  pipe  of  unequal  bore,  in  different  parts  it  is  obvious 
that  the  same  quantity  of  water  must,  in  a  given  time,  flow  through 
the  smaller  parts  of  the  tube  as  through  the  larger :  it  must  therefore 
low  proportionally  faster. 


PHENOMENA    OF    RIVERS.  131 

261.  This  proposition  supposes  the  fluid  to  move  free  of  all  resist- 
ance, and  hence  it  can  never  hold  accurately  true  in  practice.     In 
every  canal  or  river,  the  velocity  of  the  surface  is  always  greater 
than  that  of  any  other  part,  being  less  retarded  by  the  friction  of  the 
bottom  and  sides ;  and  in  a  tube,  the  particles  near  the  axis  always 
move  most  rapidly. 

It  is  of  consequence  to  avoid  all  unnecessary  expansions,  as  well  as 
contractions,  in  pipes  or  canals,  since  there  is  always  a  useless  expense 
of  force  in  restoring  the  velocity  which  is  lost  in  the  wider  parts. 

262.  The  phenomena  of  RIVERS  have  sometimes  been  explained 
on  the  supposition  that  rivers  are  bodies  falling  freely  down  inclined 
planes.     But  the  conclusions  deduced   from  this  doctrine,  are  so 
at  variance  with  experience,  as  to  be  of  no  value.     Were  every 
part  of  the  bed  of  a  river  uniform,  like  a  tube,  the  channel  or  por- 
tion which  moves  with  the  greatest  velocity,  would  be  in  the  center 
of  the  surface ;  but  inequalities  in  the  sides  and  bottom  usually  throw 
it  out  of  the  center  and  incline  it  to  one  side  or  the  other.     The  in- 
creased velocity  of  a  stream  during  a  freshet,  while  the  stream  is  con- 
fined within  its  banks,  exhibits  something  of  the  acceleration  which 
belongs  to  bodies  falling  freely  down  an  inclined  plane.     It  presents 
the  case  of  a  river  flowing  upon  the  top  of  another  river,  and  conse- 
quently meeting  with  much  less  resistance  than  when  it  runs  upon 
the  rough  uneven  surface  of  the  earth  itself.     The  augmented  force 
of  a  stream  in  a  freshet,  arises  from  the  simultaneous  increase  of  the 
quantity  of  water  and  the  velocity.     In  consequence  of  the  friction 
of  the  banks  and  beds  of  rivers,  and  the  numerous  obstacles  they 
meet  with  in  their  winding  course,  their  progress  is  very  slow,  where- 
as, were  it  not  for  these  impediments,  it  would  become  immensely 
great,  and  its  effects  would  be  exceedingly  disastrous.     A  very  slight 
declivity  is  sufficient  for  giving  the  running  motion  to  water.     Three 
inches  per  mile,  in  a  smooth,  straight  channel,  gives  a  velocity  of 
about  three  miles  per  hour.     The  Ganges,  which  gathers  the  waters 
of  the  Himalaya  Mountains,  the  loftiest  in  the  world,  at  the  distance 
of  eighteen  hundred  miles  from  its  mouth,  is  only  eight  hundred  feet 
above  the  level  of  the  sea, — that  is,  about  twice  the  height  of  Sjt. 
Paul's  church  in  London ;  and  to  fall  these  eight  hundred  feet,  in  its 
long  course,  the  water  requires  more  than  a  month.     The  great  river 


132  HYDROSTATICS. 

Magdalena  in  South  America,  running  for  a  thousand  miles  between 
two  ridges  of  the  Andes,  falls  only  five  hundred  feet  in  all  that  dis- 
tance. 

263.  The  velocity  with  which  a  fluid  issues  from  a  small  orifice  in 
the  bottom  or  side  of  a  vessel,  kept  constantly  full,  is  equal  to  that 
which  a  heavy  body  would  acquire,  by  falling  from  the  level  of  the 
surface  to  the  level  of  the  orifice. 

In  the  construction  of  water  works,  it  is  customary  to  conduct 
the  stream,  or  such  a  part  of  it  as  is  required,  into  a  cubical  cistern, 
and  to  let  it  issue  from  the  side  of  this,  near  to  the  bottom,  and  thus 
fall  upon  the  main  wheel.  Instead  of  admitting  the  water  to  the 
wheel  in  this  manner,  it  has  sometimes  been  supposed  that  an  advan- 
tage might  be  gained  by  letting  the  water  fall  down  a  height  equal  to 
that  of  the  top  of  the  cistern,  perpendicularly  upon  the  wheel,  on  the 
supposition  that  we  might  thus  avail  ourselves  of  the  force  acquired 
by  the  water  in  falling.  But  according  to  the  preceding  proposition, 
the  force  would  be  the  same  whether  the  water  issued  from  the  cis- 
tern and  thus  applied  itself  to  the  wheel,  or  whether  it  fell  upon  the 
wheel  from  a  height  equal  to  that  of  the  surface  of  the  water  in  the 
reservoir  above  the  orifice.  This  is  true  in  theory;  but  in  practice 
it  would  be  found  more  advantageous  to  take  the  water  out  of  the 
cistern,  since  the  force  of  water  falling  through  the  air  is  considera- 
bly diminished  by  the  resistance  of  the  air. 

264.  The  quantities  of  water  which  issue  from  orifices  of  the  same 
dimensions,  in  the  side  of  a  cistern  or  column,  are  proportional  to  the 
square  roots  of  their  depths  below  the  surface  of  the  fluid. 

According  to  the  last  proposition,  the  velocities  are  equal  to  those 
acquired  by  bodies  falling  freely  through  the  depths  of  the  orifices ; 
but  the  velocities  acquired  by  falling  bodies  are  as  the  square  roots 
of  the  spaces ;  that  is,  the  velocities  are  proportional  to  the  square 
roots  of  the  depths ;  and  since  the  quantities  must  evidently  vary  as 
the  velocities,  therefore,  the  quantities  discharged  by  orifices  of  the 
same  size  at  different  depths  are  as  the  square  roots  of  their  depths. 

Accordingly,  an  orifice  sixteen  inches  from  the  surface  will  dis- 
charge twice  as  much  in  a  given  time  as  one  four  inches  deep ;  and 


LAWS    OF    SPOUTING    FLUIDS.  133 

in  order  to  draw  off  from  a  given  cistern  four  times  as  much  water  as 
before,  we  must  place  the  orifice  or  gate  sixteen  times  as  deep.  A 
gate  opened  in  a  reservoir  at  the  depth  of  64  inches,  will  discharge 
only  four  times  as  much  as  it  would  at  the  depth  of  4  inches. 

265.  If  a  cylindrical  or  prismatic  vessel,  of  which  the  horizontal 
section  is  every  where  the  same,  is  filled  with  fluid,  and  empties  itself 
by  an  orifice,  the  velocity  with  which  the  surface  descends,  and  also 
the  velocity  with  which  the  water  issues,  is  uniformly  retarded. 

The  velocity  with  which  the  surface  descends  is  proportional  to 
that  with  which  the  fluid  issues  from  the  orifice,  and  therefore  is  as 
the  square  root  of  the  depth.  But  the  velocities  of  bodies  projected 
perpendicularly  upwards  are  in  the  same  ratio  to  their  spaces,  and 
therefore  a  body  projected  perpendicularly  upwards  is  in  the  same 
relative  circumstances  as  the  descending  surface  of  the  fluid ;  and 
as  the  projected  body  is  uniformly  retarded,  the  same  is  true  of  the 
descending  surface. 

On  this  principle  is  constructed  the  Clepsydra,  or  water-clock. 
Since  the  descent  of  the  surface  is  uniformly  retarded,  the  spaces 
which  it  describes  in  equal  times,  reckoning  from  the  bottom,  are  as 
the  odd  numbers  1,  3,  5,  7,  &c.;  and  if  a  cylindrical  vessel  of  water 
be  furnished  with  an  oriffce  at  the  bottom  which  will  exactly  discharge 
the  whole  column  in  twelve  hours,  and  the  sides  of  the  vessel  be  di- 
vided into  spaces  corresponding  to  the  foregoing  numbers,  the  suc- 
cessive heights  of  the  column  become  measures  of  time. 

206.  If  we  accurately  mark  the  time  in  which  a  cylindrical  or  pris- 
matic vessel,  whose  horizontal  section  is  every  where  the  same,  dis- 
charges itself  to  the  level  of  a  given  orifice,  and  then  draw  off  for  the 
same  time,  keeping  the  vessel  constantly  full,  we  shall  obtain  double 
the  quantity  of  fluid  in  the  latter  case  as  in  the  former. 

When  the  vessel  is  kept  constantly  full,  the  velocity  at  the  orifice 
(and  of  course  the  quantity  discharged)  continues  uniformly  the  same 
as  at  first;  and  since  the  circumstances  of  this  case  are  exactly  analo- 
gous .to  those  of  a  body  projected  perpendicularly  upwards ;  and 
since,  if  a  body  thus  projected  were  to  continue  to  ascend  with  the 
first  velocity,  it  would  pass  over  a  space  twice  as  great  in  the  same 


134  HYDROSTATICS. 

time  as  when  uniformly  retarded ;  therefore,  the  truth  of  the  propo- 
sition is  manifest. 

267.  A  fluid  spouting  from  the  side  of  a  vessel,  describes  the  curve 
of  a  parabola. 

The  fluid  is  precisely  in  the  same  circumstances  as  a  projectile  ac- 
ted on  by  the  force  of  projection  (viz.  the  pressure  of  the  incum- 
bent fluid)  and  by  the  force  of  gravity.  Therefore,  according  to 
Art.  83.  it  describes  the  curve  of  a  parabola.  As  in  the  case  of 
other  projectiles,  the  proposition  holds  good,  whatever  may  be  the 
angle  of  elevation  of  the  jet. 

268.  When  a  fluid  spouts  from  the  side  of  a  perpendicular  col- 
umn its  random  or  horizontal  distance  will  be  the  greatest  when  it 
spouts  from  the  center,  and  it  will  be  equal  at  equal  distances  from 
the  center  above  and  below. 

The  lower  parts  of  the  column  being  subjected  to  the  strongest 
pressure,  namely,  that  of  the  incumbent  column,  we  might  suppose 
that  the  lower  the  orifice,  the  greater  would  be  the  random ;  but  we 
must  recollect,  that  such  a  spout  would  reach  the  plane  sooner  than 
those  at  a  higher  elevation. 

269.  The  term  FRICTION  is  applied  to  the  obstruction  occasioned 
to  the  passage  of  fluids  in  the  same  manner  as  it  is  to  solids ;  and  it 
exists  to  such  an  extent  as  to  become  an  object  of  considerable  in- 
convenience in  practice.     It  can  be  obviated  only  by  making  the 
conveying  pipe  of  much  larger  dimensions  than  would  otherwise  be 
necessary,  so  as  to  allow  the  free  passage  of  a  sufficient  quantity  of 
fluid  through  the  center  of  the  pipe,  while  a  ring  or  hollow  cylinder  of 
water  is  to  be  considered  to  be  at  rest  all  around  it.     Other  circumstan- 
ces beside  friction  likewise  tend  to  diminish  the  quantity  of  fluid  which 
would  otherwise  pass  through  pipes, — such  as  the  existence  of  sharp 
or  right  angled  turns  in  them,  permitting  eddies  or  currents  to  be 
formed,  or  not  providing  for  the  eddies  or  currents  that  form  natural- 
ly* by  suiting  the  shape  of  the  pipe  to  them.     It  follows,  therefore, 
that  whenever  a  bend  or  turn  is  necessary  in  a  water  pipe,  it  should 
be  made  in  as  gradual  a  curve  or  sweep  as  possible ;  that  the  pipe 
should  not  only  be  sufficiently  capacious  to  afford  the  necessary  sup™ 


CAPILLARY   ATTRACTION.  135 

ply,  but  should  be  of  an  uniform  bore  throughout,  and  free  from  all 
projections  or  irregularities  against  which  water  can  strike,  and  form 
eddies  or  reverberations,  since  these  will  impede  the  progress  of  the 
fluid  as  effectually  as  the  most  solid  obstacles. 

270.  An  unexpected  facility  is  gained  in  the  discharge  of  a  fluid 
from  the  bottom  or  side  of  a  vessel,  by  applying  a  pipe  to  the  orifice. 
On  account  of  the  friction  known  to  occur  in  the  passage  of  a  fluid 
through  a  tube,  it  might  be  supposed  that  a  simple  orifice  made  in  the 
vessel  might  fce  more  favorable  to  the  discharge  of  the  fluid  than  an 
opening-  prolonged  by  a  tube ;  but  it  has  been  found  by  experiment, 
that  a  vessel  of  tin,  with  a  smooth  hole  formed  in  its  bottom,  did  not 
discharge  water  as  rapidly  as  another  containing  the  same  weight  of 
water,  and  an  orifice  of  the  same  dimensions,  to  which  a  short  pipe 
was  applied.  By  varying  the  length  of  the  pipe,  it  is  found  that  when 
its  length  is  twice  its  diameter,  it  produces  the  most  rapid  discharge, 
delivering,  in  this  case,  82  quarts  of  water  in  100  seconds,  while  the 
simple  hole  delivered  but  62  quarts  in  the  same  time.  If,  however, 
the  pipe  projects  into  the  vessel,  the  quantity  discharged  is  diminished 
instead  of  being  increased  by  the  pipe. 


CHAPTER  III. 

OF  CAPILLARY  ATTRACTION,  OF  THE  RESISTANCE  OF   FLUIDS, 
AND  OF  WAVES. 

Capillary  Attraction. 

271.  The  definition  of  a  fluid,  proceeds  on  the  supposition  that 
fluids  are  destitute  of  cohesion,  and  that  their  particles  move  among 
themselves  without  the  slightest  impediment.  All  liquids,  however, 
have  in  fact  more  or  less  cohesion  or  mutual  attraction  among  their 
particles.  This  is  apparent  in  their  forming  drops,  and  in  the  viscidi 
ty  of  certain  liquids,  as  oil  and  tar,  which  on  account  of  this  property 
are  sometimes  denominated  semi-fluids.  It  is  owing  to  this  property 
that  water  so  readily  forms  itself  into  drops,  and  that  its  surface, 
when  viewed  in  a  small  cup  or  wine  glass,  appears  convex.  Both  of 
these  properties  are  still  more  observable  in  quicksilver,  which,  when 
poured  on  a  table,  forms  numerous  globules  of  a  perfectly  spherical 


136  HYDROSTATICS. 

figure  ;  and  the  convex  figure  of  the  surface,  as  seen  in  a  wine  glass 
is  very  striking.  When  we  dip  a  glass  tube  into  water,  it  comes  out 
covered  with  drops  of  the  fluid,  which  are  held  by  the  attraction  of 
the  glass  for  water ;  but  the  tube  when  dipped  into  quicksilver  comes 
out  dry,  because  the  cohesion  between  the  particles  of  quicksilver 
for  one  another  is  greater  than  the  mutual  attraction  that  "exists  be- 
tween the  metal  and  the  glass.  Hence,  a  solid  body  when  immer- 
sed in  a  fluid,  is  sometimes  wet  by  it  and  sometimes  not,  according 
as  the  attraction  between  the  solid  and  the  fluid  is  greater  or  less  than 
that  which  exists  between  the  particles  of  the  fluid  for»one  another. 

272.  CAPILLARY  ATTRACTION  is  the  attraction  which  causes  the 
ascent  of  fluids  in  small  tubes. 

The  tubes  must  be  less  than  one  tenth  of  an  inch  in  diameter,  and 
tubes  whose  bores  are  no  larger  than  a  hair,  (capillus,)  present  the 
phenomenon  the  more  strikingly.  But  though  the  rise  of  water  above 
its  natural  level  is  most  manifest  in  small  tubes,  it  appears,  in  a  de- 
gree, in  all  vessels  whatsoever,  by  a  ring  of  water  formed  around 
the  sides,  with  a  concavity  upwards. 

273.  When  small  tubes,  open  at  both  ends,  are  immersed  perpen- 
dicularly in  any  liquid,  the  liquid  rises  in  them  to  a  height  which  is 
inversely  as  the  diameter  of  the  bore.     Though  tubes  of  glass  are 
usually  employed  in  experiments  on  this  subject,  yet  the  tubes  made  of 
any  other  material,  exhibit  the  same  property.     Nor  does  the  thick- 
ness of  the  solid  part  of  the  tube,  or  its  quantity  of  matter,  make  the 
least  difference,  the  effect  depending  solely  on  the  attraction  of  the 
surface,  and  consequently  extending  only  to  a  very  small  distance. 

Fluids  rise  in  a  similar  manner  between  the  plates  of  glass,  metal, 
Sic.  placed  perpendicularly  in  the  fluids  and  near  to  one  another. 
If  the  plates  are  parallel,  the  height  to  which  a  fluid  will  rise  is  in- 
versely as  the  distance  between  the  plates ;  and  -the  whole  ascent  is 
just  half  that  which  takes  place  in  a  tube  of  the  same  diameter.  If 
the  plates  be  placed  edge  to  edge,  so  as  to  form  an  angle,  and  they 
be  inynersed  in  water,  with  the  Jine  of  their  intersection  vertical 
the  water  will  ascend  between  them  in  a  curve  having  its  vertex  at 
the  angle  of  intersection. 


CAPILLARY    ATTRACTION. 


13* 


274.  Various  Phenomena  in  nature  and  art  are  explained  upon  the 
principles  of  capillary  attraction.     Capillary  action  is  not  confined  to 
tubes,  but  is  exerted  among  all  substances  which  are  perforated  by 
pores,  or  subdivided  by  fissures  or  interstices.     On  this  power  de- 
pend chiefly  the  functions  of  the  excretory  vascular  system  in  plants 
and  animals,  and  hence  also  the  ascent  of  humidity  thiough  the  shiv- 
ered fragments  of  rocks,  unglazed  pottery,  gravel,  earth,  and  sand. 
Thus  if  the  pores  of  the  human  skin  (which  are  known  to  be  exceed- 
ingly small)  are  estimated  at  the  TTJ\7  part  of  an  inch  in  diameter, 
they  will  support  the  fluids  that  circulate  through  them  to  the  height 
of  120  inches,  or  ten  feet,  or  higher  than  is  required  for  the  animal 
system.     The  ascent  of  the  sap  in  trees  has  usually  been  ascribed 
to  capillary  attraction,   their  circulating  vessels  being  a  congeries  of 
small  tubes ;  but  physiologists^  now  maintain  that  this  action  is  de- 
pendent not  on  the  mechanical  structure,  but  upon  something  which 
they  denominate  the  living  principle  of  vegetables. 

275.  According  to  Professor  Leslie,  if  a  soil  of  gravel  contains 
pores  100th  part  of  an  inch  in  diameter,  water  will  ascend  in  it  by 
capillary  action  more  than  four  inches ;  and  supposing  the  particles  of 
coarse  sand  to  have  interstices  of  500th  part  of  an  inch,  the  water 
would  rise  through  a  bed  of  sixteen  inches ;  and  if  the  pores  were 
diminished  to  the  10,000th  part  of  an  inch,  water  would  rise  twenty 
five  and  a  half  feet.     Hence,  in  agriculture,  are  derived  the  advan- 
tages of  deep  and  perfect  tillage ;  since  the  more  effectually  a  soil  is 
pulverized,  the  better  fitted  it  is  to  raise  and  retain  water  near  the 
surface. 

Several  familiar  examples  of  capillary  attraction  may  be  added. 
A  piece  of  sponge,  or  a  lump  of  sugar,  touching  water  by  its  lowest 
corner,  soon  becomes  moistened  throughout.  The  wick  of  a  lamp 
lifts  the  oil  to  supply  the  flame,  to  the  height  of  several  inches.  A 
capillary  glass  tube  bent  in  the  form  of  a  syphon,  and  having  its 
shorter  end  inserted  into  a  vessel  of  water,  will  fill  itself  and  deliver 
over  the  water  in  drops.  A  lock  of  thread  or  of  candle  wick,  in- 
serted in  a  vessel  of  water  in  a  similar  manner,  with  one  end  hanging 
over  the  vessel,  will  exhibit  the  same  result.  An  immense  weight 
or  mass  may  be  raised  through  a  small  space,  first  by  stretching  a* 
dry  rope  between  it  and  a  support  and  then  wetting  the  rope, 

18 


138  HYDROSTATICS. 

Resistance  of  Fluids. 

276.  The  resistance  which  a-  plane  surface  meets  with  while  it 
moves  in  a  fluid,  in  a  direction  perpendicular  to  its  plane,  is  pro- 
portioned to  the  square  of  its  velocity. 

Hence,  a  boat  in  the  water  encounters  but  little  resistance  when 
moving  slowly,  but  the  resistance  increases  rapidly  as  the  speed  is 
augmented.  Doubling  the  velocity  increases  the  resistance  fourfold ; 
tripling  the  velocity  renders  the  resistance  nine  times  what  it  was 
before.  This  proposition  is  found  to  hold  good  in  practice,  where 
the  velocity  is  very  small,  as  in  the  motions  of  boats  or  vessels  in 
water;  but  when  the  velocity  becomes  very  great,  as  that  of  a  can- 
non ball,  the  resistance  increases  in  a  much  higher  ratio  than  as  the 
square  of  the  velocity.  Since  action  a^id  reaction  are  equal,  it  makes 
BO  difference,  in  the  foregoing  proposition,  whether  we  consider  the 
plane  in  motion  and  the  fluid  at  rest,  or  the  fluid  in  motion  and  striking 
against  the  plane  at  rest. 

On  account  of  the  rapidity  with  which  the  resistance  increases  as 
the  velocity  is  augmented,  when  a  vessel  or  a  steam-boat  is  moving 
in  water,  it  is  only  a  comparatively  moderate  velocity  that  can  possi- 
bly be  given  to  it.  A  vessel  driven  by  a  wind  which  moves  60  miles 
an  hour,  is  not  carried  forward  faster  than  at  the  rate  of  12  or  14 
miles  per  hour.  Steam-boats  are  sometimes  urged  forward  at  the 
rate  of  16  miles  an  hour;  but  to  gain  the  additional  speed  over  and 
above  12  miles,  requires  a  great  expenditure  of  force.  If  a  steam 
engine  of  20  horse  power  give  a  motion  of  4  miles  an  hour,  it  would 
require  one  of  180  horse  power  to  increase  the  speed  to  12  miles  an 
hour.  But,  it  must  be  observed  that  the  resistance  decreases  as  fast 
when  the  velocity  is  diminished,  as  it  increases  when  the  velocity  is 
augmented ;  and  consequently,  that  canals  may  have  the  advantage 
over  railways,  when  heavy  articles  are  to  be  transported  by  very 
slow  motions,  although  railways,  encountering  only  the  resistance  of 
the  air  instead  of  water,  have  greatly  the  advantage  when  the  motion 
is  swift. 

It  follpws  from  the  foregoing  doctrine  that  a  body  descending  free- 
ly through  the  air  by  gravity  for  a  great  distance,  does  not  continue 
to  be  accelerated  throughout  the  whole  distance,  but  is  finally  brought, 
by  the  resistance  of  the  air,  to  a  uniform  motion. 


WAVES.  139 

277.  The  motion  of  fluids  in  pipes  and  otherwise,  is  modified  so 
much  by  the  impediments  arising  from  friction  against  the  sides  of 
the  pipe  or  channel,  from  resistance  of  the  air,  and  from  more  or 
less  cohesion  in  the  fluid  itself,  that  the  foregoing  principles  dedu- 
ced from  theory  require  great  allowances  to  be  made  when  applied 
to  practice.  The  nature  of  these  impediments,  however,  is  so  well 
understood  that  the  theoretical  principles  of  hydraulics,  may  be  re- 
duced to  practice  without ,  an  error  exceeding  one  fifth  or  evven  one 
tenth  of  the  whole. 

278.  Undulation  of  Fluids  and  the  formation  of  Waves. 
When  the  surface  of  water  is  pressed  upon  unequally,  in  parts 
contiguous  to  one  another,  the  columns  most  pressed  are  shortened, 
and  sink  beneath  the  natural  level  of  the  surface,  while  those  that 
are  least  pressed  are  lengthened,  and  rise  above  that  level.  As  soon 
as  the  former  columns  have  sunk  to  a  certain  depth,  and  the  latter 
have  risen  to  a  certain  height,  their  motions  are  reversed,  and  con- 
tinue so,  until  the  columns  that  were  at  first  most  depressed  have 
become  most  elevated,  and  those  that  were  most  elevated  have  be- 
come most  depressed.  The  alternate  elevations  and  depressions  of 
the  surface  of  a  body  of  water,  produced  by  a  force  acting  unequal- 
ly on  the  surface,  are  called  waves.  The  water  in  the  formation  of 
waves  has  a  vibratory  or  reciprocating  motion,  both  in  a  horizontal 
and  in  a  vertical  direction,  by  which  it- passes  from  the  columns  that 
are  shortened  to  those  that  are  lengthened,  and  returns  again  in  the 
opposite  direction.  Progressive  motion  is  not  necessary  to  undu- 
lation. 

279.  Sir  Isaac  Newton  first  observed  the  analogy  between  the 
motions  of  waves  and  the  vibrations  of  a  column  of  water  in  a  re- 
curved tube,  and  upon  this  analogy  he  founded  his  theory  of  waves. 
Let  AFGB  (Fig.  67.)  be  a  bent  lube,  of  equal 
bore  throughout,  having  its  sides  parallel  and 
perpendicular  to  the  horizon.  Suppose  it  to 
be  filled  with  water  or  any  fluid  to  the  height 
MM7.  .  By  any  pressure  applied  at  M',  let  the 
column  be  depressed  to  N'  and  raised  to  E  in 
the  oppositee  arm.  The  pressure  being  re- 
moved, the  longer  column  EF  will  preponder- 
ate, and  seek  to  regain  its  original  level,  but 


140  HYDROSTATICS. 

the  ascending  column  will  not  stop  at  M',  but  on  account  of  its  iner- 
tia will  ascend  to  E',  that  is,  to  the  same  height  as  that  from  which  it 
descended  on  the  other  side.  It  will  now  descend  again,  and  these 
reciprocal  motions  will  continue  until  destroyed  by  the  natural  im- 
pediments to  motion.  On  account  of  these,  each  successive  vibra- 
tion is  shorter  than  the  preceding,  but  all  of  them,  like  those  of  a 
pendulum,  are  performed  in  equal  times ;  for  the  moving  force  is  ob- 
viously proportioned  to  the  column  EM,  that  is,  to  the  space  through 
which  the  whole  column  vibrates ;  and  when  the  forces  are  as  the 
spaces,  the  times  are  equal. 

280.  Now  when  the  surface  of  water  is  smooth  and  at  rest,  if  any 
force  (as  the  action  of  the  wind  or  the  fall  of  a  stone)  depress  that 
surface  in  any  particular  place,  the  contiguous  water  will  necessarily 
rise  al]  around  that  place.     The  water  which  has  thus  been  elevated, 
descends  soon  after  in  consequence  of  its  gravity ;  and  by  the  time 
it  has  reached  the  original  level,  it  will  have  acquired  velocity  suffi- 
cient to  carry  it  lower  than  that  level ;  therefore,  it  now  acts  as  an- 
other original  moving  force,  in  consequence  of  which,  the  water  will 
be  raised  on  both  sides  of  it.     And  for  the  same  reason,  the  descent 
of  those  elevated  parts  will  produce  other  elevations  contiguous  to 
them,  and  so  on.     Thus  the  alternate  rising  and  falling  of  the  water 
in  ridges,  will  expand  all  around  the  original  place  of  motion ;  but 
as  they  recede  from  that  place,  so  the  ridges,  as  well  as  the  adjoin- 
ing hollows,  grow  smaller  and  smaller  until  they  vanish.     This  dim- 
inution of  size  is  produced  by  three  causes,  namely,  by  the  want  of 
perfect  freedom  of  motion  amongst  the  particles  of  water,  by  the  re- 
sistance of  the  air,  and  by  the  remoter  ridges  being  larger  in  diame- 
ter than  those  which  are  nearer. 

281.  From  a  variety  of  experiments  and  observations,  it  appears 
that  the  utmost  force  of  the  wind  cannot  penetrate  a  great  way  into 
the  water ;  and  that  even  in  violent  storms  the  water  of  the  sea  is 
slightly  agitated  at  the  depth  of  twenty  feet  below  the  usual  level,  and 
probably  not  moved   at  all  at  the  depth  of  thirty  feet.     Therefore, 
the  actuaj  displacing  of  the  water  by  the  wind  cannot  be  supposed  to 
reach  nearly  so  low  ;  and  hence  it  would  seem  that  the  greatest  waves 
rould  not  be  so  very  high  as  they  are  often  represented  by  navigators. 
JFJut  it  must  be  observed,  that  in  storms  waves  increase  to  an  enor- 


QUESTIONS.  141 

mous  size  from  the  accumulation  of  waves  upon  waves ;  for,  as  the 
wind  is  continually  blowing,  its  action  will  raise  a  wave  upon  another 
wave,  and  a  third  wave  upon  a  second,  in  the  same  manner  as  it  raises 
a  wave  upon  the  flat  surface  of  the  water.  In  fact,  at  sea,  a  variety 
of  waves  of  different  sizes  are  frequently  seen  one  upon  the  other, 
especially  while  the  wind  is  actually  blowing.  When  it  blows  fresh, 
the  tops  of  the  waves,  being  lighter  and  thinner  than  the  other  parts, 
are  impelled  forward,  broken,  and  turned  into  a  white  foam,  particles 
of  which,  called  spray,  are  carried  to  a  great  distance.  Whilst  the 
depth  of  the  water  is  sufficient  to  allow  the  oscillation  to 'proceed  un- 
disturbed, the  waves  have  no  progressive  motion,  and  are  kept,  each 
in  its  place,  by  the  action  of  the  waves  that  surround  it.  But  if  by 
a  rock  rising  near  to  the  surface,  or  by  the  shelving  of  the^fi£re^ 
oscillation  is  prevented  or  much  retarded,  the  waves  in  the  deep 
ter  are  not  balanced  by  those  in  the  shallower,  and  therefore  acquire 
a  progressive  motion  in  this  last  direction,  and  form  breakers.  Hence 
it  is  that  waves  always  break  against  the  shore,  whatever  be  the  di- 
rection of  the  wind. 

282.   Questions  in   Hydrostatics. 

1.  In  a  Hydrostatic  Press,  (Fig.  60.)  the  height  of  the  small  col- 
umn AB  on  which  the  power  acts  is  2  feet  above  the  bottom  of  the 
larger  piston  CD  ;  the  diameter  of  the  cylinder  AB  is  one  inch, 
and  of  the  cylinder  CD  1  foot.     By  means  of  a  screw  turned  by  a 
lever,  a  man  can  exert  a  force  on  A  equal  to  500  Ibs.     What  amount 
of  pressure  can  he  apply  with  the  aid  of  this  press,  combining  his 
own  strength  with  the  pressure  of  the  column  of  water  AB  ? 

Ans.  72098.17  Ibs. 

2.  A  Junk  Bottle,  whose  lateral  surface  contained  50  square  inch- 
es, was  let  down  into  the  sea  500  fathoms,  (3000  feet :)  What  press*- 
ure  would  the  sides  of  the  bottle  sustain,  no  allowance  being  made 
for  the  increased  specific  gravity  of  the  sea  water  ? 

Ans.  65104.166  Ibs. 

3.  A  Greenland  Whale  sometimes  has  a  surface  of  3600  square 
feet :  What  pressure  would  he  bear  at  the  depth  of  800  fathoms  r 

Ans.  1080,000,000  Ibs.  or  more  than  482142  tons. 

4.  A  mineral  weighs  960  grains  in  air,  and  739  grains  in  water ; 
What  is  its  specific  gravity  ?  Ans.  4.343. 


142  HYDROSTATICS. 

5.  What  are  the  respective  weights  of  two  equal  cubical  masses  of 
gold  and  cork,  each  measuring  2  feet^on  its  linear  edge  ? 

Ans.   The  gold  weighs  9625  Ibs.  =4.278  tons;  the  cork  weighs 
120  Ibs. 

6.  On  one  of  the  peaks  of  the  Alps,  is  a  single  mass  of  granite 
rock  of  nearly  a  globular  shape,  which  is  estimated  by  measure  to 
contain  5049  cubic  feet.     The  whole  mass  is  so  nicely  balanced  on 
its  center  of  gravity,  that  a  single  man  may  give  it  a  rocking  motion. 
By  trial  made  upon  a  small  fragment,  its  specific  gravity  was  found 
to  be  2.6  :  What  is  its  weight?  Ans.  366.277  tons. 

7.  Wishing  to  ascertain  the  exact  number  of  cubic  inches  in  a  very 
irregular  fragment  of  stone,  I  ascertained  its  loss  of  weight  in  water 
$0  be  5.346  ounces:  Required  its  dimensions  ? 

Ans.  9.238  cubic  inches. 


143 


PART   III. — PNEUMATICS. 

CHAPTER  I. 

OF  THE  MECHANICAL  PROPERTIES  OF  AIR. 

283.  PNEUMATICS  is  that  branch  of  Mechanics,  which  treats  of  the 
equilibrium  and  motion  of  elastic  fluids. 

Those  laws  of  equilibrium  which  are  founded  on  the  peculiar  na- 
ture of  fluids,  arising  from  the  mobility  of  their  particles,  are  equally 
applicable  to  Hydrostatics  and  Pneumatics.  But  certain  additional 
properties  result  from  the  elasticity  of  vapors  and  gases,  which  may 
be  conveniently  considered  under  the  latter  head. 

284.  Vapors  are  elastic  fluids  which  are  produced  from  liquid* 
or  solid  bodies,  by  the  agency  of  heat,  and  which  readily  become 
liquid  or  solid  again  on  the  application  of  cold.     Thus  steam  is  raised 
from  boiling  water,  and  is  again  easily  condensed  by  cold  into  the 
liquid  state.     Gases  are  permanently  elastic  fluids.     They  are  never 
met  with  in  nature,  either  in  the  liquid  or  solid  state,  and  it  is  only  by 
means  of  extraordinary  degrees  of  cold  or  pressure,  that  they  caff 
be  made  to  give  up  their  elasticity  and  become  liquids.     Atmospheric 
air  is  a  body  of  this  class ;  and  since  air  and  steam  are,  with  slight 
exceptions,  the  only  elastic  fluids  employed  as  mechanical  agents? 
it  is  to  these,  chiefly,  that  our  attention-  will  be  devoted. 

285.  The  properties  of  air  may  be-  exhibited  under  the  form  of 
a  few  simple  propositions. 

(1.)  Jlir  is  material. 

The  two  essential  properties  of  matter  are  extension  and  impene- 
trability. That  air  has  extension,  needs  no  proof.  That  it  is  im- 
penetrable, or  has  the  property  of  excluding  all  other  matter  from 
the  space  which  it  occupies,  is  proved  by  experiment.  Thus,  if 
we  depress  in  water  a  tall  jar,  or  a  tumbler,  we  shall  find  that  the 
water  rises  only  through  a  certain  part  of  the  vessel,  to  whatever 
depth  we  immerse  it;  and  if,  to  a  hollow  cylinder,  made  smooth  and 
closed  at  the  bottom,  we  fit  closely  a  stopper  or  solid  cylinder,  called 


144 


PNEUMATICS. 


a  piston,  moving  freely  in  it,  on  applying  the  piston,  110  force  wil 
enable  us  to  bring  it  into  contact  with  the  bottom  of  the  cylinder, 
unless  we  permit  the  air  within  it  to  escape.  Two  other  properties 
exhibited  by  air,  likewise  indicate  that  it  is  material :  these  are  iner- 
tia and  weight.  The  inertia  of  air  is  manifested  by  the  resistance  it 
opposes  to  bodies  moving  in  it ;  as,  for  example,  an  open  umbrella 
moved  through  the  air,  in  a  direction  parallel  with  the  staff;  and  the 
weight  of  the  air  is  shown  by  the  fact  that  a  vessel,  as  a  bottle',  from 
which  the  air  has  been  withdrawn  (by  methods  to  be  described  here- 
after) weighs  less  than  before.  A  vessel  of  the  capacity  of  a  wine 
quart,  weighs  about  eighteen  grains  less  after  the  air  is  exhausted, 
than  before.  One  hundred  cubic  inches  of  air  weighs  thirty  grains 
and  a  half. 

(2.)  Air  is  a  fluid. 

This  property  is  manifested  not  only  by  the  great  mobility  of  its 
parts,  but  also  by  the,  distinguishing  property  of  fluids,  viz.  that  any 
portion  of  air  at  rest,  presses  and  is  pressed  equally  in  all  directions; 
and  that  a  pressure  or  blow  applied  to  any  part,  is  propagated  through 
the  whole  mass,  and  affects  every  part  alike. 

(3.)  Mr  is  an  ELASTIC  fluid. 

Thus,  when  an  inflated  bladder  is  compressed,  it  immediately  re- 
stores itself  to  its  former  situation.  Indeed,  since  air,  when  com- 
pressed, restores  itself,  or  tends  to  restore  itself,  with  the  same  force 
as  that  with  which  it  is  compressed,  it  is  a  perfectly  elastic  body. 


286.  Before  we 
proceed  further,  it  is 
necessary  for  the 
learner  to  be  made 
acquainted  with  the 
apparatus,  by  which 
the  mechanical  prop- 
erties of  air  are  illus- 
trated. 

The  Mr  Pump. 

The  Air  Pump 
(Fig.  68.)  is  an  in- 
strument used  for  the 


Fig.  68. 


tfECHAJUCAL    PROPERTIES    Of    AIR. 

purpose  of  exhausting  the  air  from  any  given  space.  Though  of 
several  different  forms,  yet  the  most  common  construction  is  that 
represented  in  Fig.  68.  The  chief  parts  are  the  plate  A,  the  bar- 
rels EE,  and  the  pipe  or  canal  C,  leading  from  the  plate  to  the 
barrels.  The  glass  vessels  which  are  set  upon  the  plate,  are  called 
in  general  receivers.  A  guage  is  sometimes  employed  (as  repre- 
sented by  D  in  the  figure)  to  indicate  the  degree  of  exhaustion ;  but 
the  nature  of  this  appendage  will  be  better  understood  hereafter. 
Such  is  the  construction  of  the  air  pump  in  general ;  but  the  impor- 
tance of  this  apparatus  entitles  it  to  a  more  minute  description.  In 
order,  then,  fully  to  understand  the  principle  of  the  air  pump,  and 
other  kinds  of  apparatus  designed  for  producing  a  vacuum,  we  must 
understand  the  construction  of  valves,  and  of  the  cylinder  and  piston, 

287.  A  VALVE  is  a  contrivance  which  permits  a  fluid  to  pass  in  one 
direction,  but  prevents  its  passing  in  the  opposite  direction.  The 
clapper  seen  on  the  under  side  of  a  pair  of  bellows,  is  a  familiar  ex- 
ample of  a  valve.  The  valve  employed  in  the  air  pump,  usually 
consists  merely  of  a  strip  of  oiled  silk,  tied  over  a  small  orifice.  The 
air  by  pressing  outwards  from  the  orifice  raises  the  silk,  opens  the 
valve,  and  makes  its  escape ;  while  by  pressing  inwards  upon  the 
orifice,  it  keeps  the  strip  of  silk  close  to  the  orifice,  and  is  therefore 
prevented  from  passing  in  that  direction.  The  piston  and  cylinder  are 
exemplified  in  a  common  syringe.  It  consists  of  a  hollow  cylinder,- 
or  barrel,  to  which  is  fitted  a  short  solid  cylinder  called  the  piston, 
which  is  moved  up  and  down  the  barrel  by  means  of  a  projecting 
handle  called  the  piston-rod,  and  is  fitted  so  closely  to  the  barrel  as 
to  be  air  tight.  Suppose  now  that  the  cylinder  is  in  a  perpendicular 
position,  closed  below  but  open  above,  and  that  the  piston  rests  ort 
the  bottom.  On  drawing  up  the  piston,  the  air  above  it  is  lifted  outf 
and  the  space  below  it  is  a  vacuum.  If  a  small  orifice  be  made  in 
the  bottom  of  the  barrel,  then  as  the  piston  is  drawn  upwards,  the  air 
will  flow  in  and  no  vacuum  will  be  formed ;  and  as  the  piston  is  de- 
pressed again,  the  air  is  forced  back.  But  by  attaching  a  valve  to 
the  orifice,  we  may  admit  or  exclude  the  external  air  at  pleasure.  If 
the  strip  of  silk  be  tied  on  the  outside,  then,  on  drawing  up  the  pis- 
ton, the  air  will  not  follow,  but  the  piston  will  go  up  heavily,  since  if 
tifts  up  the  entire  weight  of  the  column  of  air  that  rests  upon  it,  (there 

19 


146 


PNEUMATICS. 


being  nothing  below  it  to  act  as  a  counterpoise,)  and  if  the  hand  be 
withdrawn  from  the  piston  rod,  the  piston  will  descend  spontaneous- 
ly. Again,  if  the  valve  be  placed  on  the  inside,  then  the  external 
air  will  follow  the  piston  as  it  rises,  and  no  vacuum  will  be  formed. 
If  now  the  piston  be  depressed,  the  air  cannot  be  expelled,  (since  the 
valve  closes  on  the  orifice  in  that  direction,)  and  the  piston  cannot  be 
forced  down  to  the  bottom  of  the  barrel,  unless  a  valve  is  placed  in 
the  piston  itself,  opening  outwards ;  in  this  case,  the  air  of  the  barrel 
may  be  expelled  by  depressing  the  piston. 

288.  We  have  been  thus  minute  in  the  description  of  the  con- 
struction of  valves,  and  of  the  cylinder  and  piston,  because  when 
these  things  are  clearly  understood,  the  learner  will  easily  compre- 
hend the  principle  of  the  air  pump,  of  the  common  house  pump,  of 
the  steam  engine,  and  of  every  other  species  of  pneumatic  apparatus. 
Let  us  now  return  to  the  air  pump. 

In  the  barrels,  two  pistons  play  up  and  down,  each  of  which  is  fur- 
nished with  a  valve  opening  upwards  into  the  open  space,  through 
which  the  piston  rods  move.  Another  valve  is  placed  at  the  bottom  of 
each  barrel,  opening  into  the  barrel.  The  piston  rods  are  indented 
bars,  to  which  a  toothed  wheel  (concealed  in  Fig.  6.8,  but  seen  in 
Fig.  69,)  is  adapted,  which,  being  turned  backwards  and  forwards 

Fig.  69. 


MECHANICAL  PROPERTIES  OF  AIR.  147 

by  means  of  the  winch  G,  (Fig.  68.)* alternately  raises  and  depresses 
the  two  pistons,  as  is  represented  in  figure  69.  Suppose  now  the 
receiver  to  be  placed  on  the  plate  of  the  pump,  one  of  the  pistons 
being  at  the  top,  and  the  other  at  the  bottom  of  the  barrel.  We  turn 
the  winch,  the  piston  rises,  and  the  air  of  the  receiver  opens  the 
valve  at  the  bottom  of  the  barrel,  and  diffuses  itself  equally  through 
the  barrel  and  the  receiver.  We  turn  the  winch  in  the  opposite  di- 
rection, the  piston  descends,  compresses  the  air  in  the  barrel  before 
it,  which,  as  it  cannot  go  back  into  the  receiver,  opens  the  valve  in 
the  piston  itself,  and  escapes  into  the  vacant  space  in  which  the  arm 
of  the  piston  moves.  This  process  is  repeated  every  time  the  piston 
rises  and  falls;  and  it  is  the  same  in  both  barrels,  two  being  employed 
for  no  other  reason  than  to  accelerate  the  process  of  exhaustion. 

289.  By  means  of  this  instrument,  we  may  obtain  very  striking 
illustrations  of  the  mechanical  properties  of  air. 

(1.)  The  pressure  of  the  air  acts  with  great  force  on  all  bodies  at 
the  surface  of  the  earth,  amounting,  as  we  shall  show  hereafter,  to 
nearly  15  pounds  upon  every  square  inch,  or  more  than  2000  pounds 
upon  a  square  foot.  Upon  so  large  a  surface,  therefore,  as  that  of 
the  human  body,  the  pressure  amounts  to  no  less  than  13  or  14  tons; 
but  being  so  uniformly  distributed  within  and  without,  and  on  all  sides, 
it  is,  when  the  air  is  at  rest,  scarcely  perceptible.  In  consequence  of 
this  pressure  the  air  insinuates  itself  into  all  fluids,  and  fills  the  pores 
of  all  solids  except  the  most  dense,  as  gold  or  platina.  The  pressure 
of  the  air  diminishes  the  tendency  of  fluids  to  pass  into  the  state  of 
vapor,  and  of  course  raises  their  boiling  point.  Warm  water,  at  a 
temperature  much  below  the  boiling  point,  will  be  set  a  boiling  under 
the  receiver  of  an  air  pump,  or  in  a  vacuum  formed  in  any  other 
way.  Indeed,  if  it  were  not  for  atmospheric  pressure,  water  )vould 
require  only  the  moderate  heat  of  72  instead  of  212  degrees  of  heat 
to  make  it  boil ;  and  the  more  volatile  fluids,  as  alcohol  and  ether, 
would  hardly  be  found  in  nature,  in  the  liquid  state. 

(2.)  The  elasticity  of  the  air  is  such,  that  the  smallest  portion  of  it 
may  be  expanded  beyond  any  known  limits,  by  removing  the  exter- 
nal pressure.  By  this  means,  a  bubble  may  be  made  to  fill  a  very 
large  space.  On  the  other  hand,  air  has  been  condensed  by  press- 
ure, until  its  density  has  been  greater  than  than  of  water,  still  retain- 


J48 


PNEUMATICS. 


Fig.  70. 


ing  the  elastic  invisible  state,  In  consequence  of  its  elasticity,  air 
is  set  in  motion  by  the  least  disturbance  of  its  equilibrium,  whether 
by  condensation  or  rarefaction,  thus  giving  rise  to  the  phenomena  of 
winds. 

(3.)  Air  is  essential  to  the  support  of  combustion,  and  to  the 
respiration  of  animals ;  and  finally,  it  is  the  principal  medium  of 
sound.  It  may  be  farther  shown,  that  the  weight  of  bodies  is  dimin- 
ished by  the  bouyancy  of  air,  (acting  on  the  same  principle  as  water, 
and  that  light  bodies  are  sustained  in  it,  in  consequence  of  its  greater 
specific  gravity,  while,  in  a  vacuum,  bodies  of  various  densities,  as  a 
guinea  and  a  feather,  fall  towards  the  earth  with  equal  velocities. 

The  Condenser. 

290.  The  condensation  of  air  is  usually  effected  by  means  of  the 
Condensing  Syringe.     This  instrument  is  a  cylinder  and  piston,  the 
cylinder  having  a  valve  opening  outwards,  while  the 

piston  is  without  a  valve.  The  principle  of  its  op- 
eration will  be  readily  understood  from  the  figure. 
Near  the  top  of  the  cylinder  is  a  small  hole  in  the 
side,  which  is  immediately  below  the  piston,  when 
this  is  drawn  up  to  the  top  of  the  cylinder.  On 
forcing  down  the  piston,  the  air  is  driven  before  it, 
and  expelled  through  the  valve  at  the  bottom.  By 
connecting  a  bottle  or  other  close  vessel  with  the 
bottom,  the  air  expelled  may  be  driven  into  that, 
its  return  being  prevented  by  the  same  valve.  The 
piston  being  drawn  up  again  above  the  opening  in 
the  cylinder,  another  similar  portion  of  air  may  be 
forced  into  the  condensing  bottle  ;  and  thus  the  pro- 
cess may  be  continued  indefinitely. 

291.  The  Condensing  Fountain  is  a  bottle,   usually  of  copper, 
partly  filled  with  water,  upon  the  surface  of  which  the  air  is  condens- 
ed by   means  of  the  condensing  syringe.     The  fluid   being  thus 
brought  under   a  strong  pressure,  it  tends  to  issue  with  great  force 
whenever  a  pipe,  that  is  inserted  in  the  bottle,  and  extends  below  the 
surface  of  the  water,  is  opened.     The  celebrated  spouting  springs  of 
Iceland,  called  the  Geysers,  in  which  water  accompanied   by  large 


MECHANICAL  PROPERTIES  OF  AIR.  149 

masses  of  rock,  is  thrown  to  the  height  of  200  feet,  ante  from  pneu- 
matic pressure  acting  upon  the  surface  of  water  in  the  interior  of  the 
earth,  the  aeriform  substance,  whatever  it  may  be,  being  produced  by 
means  of  volcanic  action. 

292.  The  Mr-Gun  is  an  instrument  in  which  condensed  air  is  sub- 
stituted as  the  moving  force  instead  of  gun-powder.     By  means  of 
a  condensing  syringe,  air  is  strongly  condensed  in  a  metallic  ball  fur- 
nished with  a  valve  at  the  mouth,  where  it  is  screwed  on  the  gun  be- 
low the  lock.     As  the  lock  is  sprung,  it  falls  upon  a  plug,  and  forces 
it  upon  the  valve,  which  suddenly  opens,  and  the  air  rushes  into  the 
barrel  of  the  gun,  and  by  its  sudden  expansion,  propels  a  ball  much 
in  the  same  manner  as  gun-powder  would  do  in  its  place. 

293.  The  Diving  Bell  is  an  apparatus  employed  for  exploring  the 
depths  of  the  sea.     It  was  formerly  made  in  the  shape  of  a  bell,  but 
is  now  more  commonly  made  square  at  the  top  and  bottom,  the  bot- 
tom being  a  little  larger  than  the  top,  and  the  sides  slightly  diverging 
from  above.     The  material  is  sometimes  cast  iron,   the  whole  ma- 
chine being  cast  in  one  piece,  and  made  very  thick,  so  that  there  is 
no  danger  either  from  leakage  or  fracture.     Sometimes  the  diving 
bell  is  made  of  planks  of  two  thicknesses,  with  sheet  lead  between 
them.     In  the   top  of  the  machine  are  placed  several  strong  glass 
lenses  for  the  admission  of  light,   such  as  are  used   in  the  decks  of 
vessels  to  illuminate  the  apartments  below. 

294.  The  diving  bell  depends  for  its  efficacy  on  that  quality  of  air, 
which  is  common  to  all  material  substances,  impenetrability;  that  is, 
the  exclusion  of  all  other  bodies  from  the  space  it  occupies.     The 
principle  may  be  illustrated  by  depressing  a  tumbler  or  jar  in  water, 
with  the  mouth  downwards:  it  will  be  seen  (Art.  285.)  that  the  water 
will  ascend  so  far  as  to  occupy  only  a  pact  of  the  capacity  of  the  ves- 
sel, the  upper  part  being  occupied  by  air.     As  the  diving  bell  de- 
scends in  the  water,  the  air  inclosed  in  it  is  subject  to  its  pressure, 
(which  increases  with  the  depth,)  and  by  virtue  of  its  elasticity,  it  will 
become  condensed  in  proportion  to  this  pressure.     Thus  at  the  depth 
of  about  thirty  four  feet,  the  hydrostatic  pressure  will  be  equal  to  that 
of  the  atmosphere,  and  consequently,  the  air  being  under  a  pressure 
equivalent  to  that  of  two  atmospheres,  it  will  be  condensed  into  one 


150  PNEUMATICS. 

half  its  original  volume.  As  the  depth  is  increased,  the  space  occu- 
pied by  the  air  in  the  bell  will  be  proportionally  diminished.  Seats 
are  furnished  for  the  workmen,  and  shelves  for  tools  and  various 
other  conveniences.  Although  at  the  depth  of  thirty  four  feet,  the 
water  would  occupy  one  half  the  capacity  of  the  vessel,  and  more  or 
less  at  different  depths,  yet  by  means  of  a  forcing  pump  or  condensing 
syringe  communicating  between  the  atmosphere  above  and  the  ma- 
chine, through  a  pipe,  air  may  be  thrown  in  so  as  to  exclude  the 
water  entirely.  .  By  the  same  means  fresh  air  may  be  conveyed  to 
the  workmen,  the  portion  of  air  rendered  impure  by  respiration  being 
at  the  same  time  suffered  to  escape  by  opening  a  stop-cock  in  the 
top  of  the  machine. 

The  Barometer. 

295.  Let  us  take  a  glass  tube,  about  three  feet  in  length,   F»g-  71 
olosed  at  one  end  and  open  at  the  other.     We  fill  the  tube 

with  quicksilver,  and  invert  it  in  a  vessel  of  the  same  fluid. 
The  column  of  quicksilver  falls  to  a  certain  height,  about 
twenty  nine  or  thirty  inches,  where,  after  vibrating  a  few 
times,  it  remains  at  rest.  The  space  in  the  tube  above  the 
quicksilver  being  void  of  air  or  any  other  substance,  it  is 
of  course  a  vacuum,  and  is  usually  denominated  the  Torri- 
cellian vacuum,  from  Torricelli,  an  Italian  philosopher,  who 
first  discovered  this  method  of  producing  a  vacuum.  Va- 
rious precautions  are  necessary,  in  order  to  preserve  this 
space  free  from  air  or  any  aeriform  substance  ;  when  these 
precautions  are  taken,  this  vacuum  is  the  most  complete  of 
any  that  we  can  command. 

296.  The  column  of  quicksilver  is  sustained  by  the  pres- 
sure of  the  atmosphere,  on  the  open  mouth  of  the  tube 
which  is  immersed  in  the  same  fluid  ;*  and  it  must  have 
the  same  weight  with  a  column  of  the  atmosphere  of  the 
same  base,  otherwise  it  would  not  be  in  equilibrium  with  it. 
We  hence  arrive  at  an  accurate  knowledge  of  the  actual 


*  As  young  learners  sometimes  find  a  dificulty  in  conceiving  clear- 
Jy  how  the  pressure  of  the  air  act?  in  this  case,  we  subjoin  a  remark 


THE    BAROMETER.  151 

weight  and  pressure  of  the  air,  since  it  is  equal  to  the  weight  of  a 
column  of  quicksilver  of  the  same  base,  thirty  inches  in  length.  The 
weight  of  such  a  cylinder  of  quicksilver  is  easily  ascertained,  and  it 
results,  that  the  pressure  of  the  air  on  every  square  inch  of  surface 
is,  as  stated  in  Art.  289,  about  15  Ibs.  or  more  than  2000  Ibs.  upon  a 
square  foot.  Since  different  fluids  balance  each  other  in  opposite 
columns  pressing  base  to  base,  when  their  heights  are  inversely  as 
their  specific  gravities,  a  column  of  water  in  the  place  of  the  mercu- 
ry would  stand  at  the  height  of  about  34  feet.  For  quicksilver  be- 
ing 13.57  times  heavier  than  water,  the  latter  column  must  be  13.57 
times  higher  than  the  other;  that  is,  30x13.57=407.1  inches 
=33.84  feet. 

297.  By  observing  from  day  to  day  the  height  of  the  column  of 
quicksilver  prepared  as  above,  we  shall  find  that  it  varies  through  a 
space  of  two  or  three  inches,  showing  that  the  atmosphere  does  not 
always  exert  the  same  pressure,  but  that  a  given  column  of  the  air  is 
sometimes  lighter  and  sometimes  heavier.     This  instrument,  there- 
fore, enables  us  to  ascertain  the  relative  weight  of  the  air  at  any  giv- 
en time,  and  hence  its  name  barometer.*     For  the  purpose  of  indi- 
cating these  variations  with  minuteness  and  precision,   a  graduated 
scale  is  attached  to  the  barometer,  divided  into  inches  and  tenths  of 
an  inch,  and  usually  extending  from  twenty  seven  to  thirty  one  in- 
ches,— a  space  which  is  more  than  sufficient  to  comprehend  all  the 
natural  variations  in  the  weight  of  the  atmosphere. 

298.  Since  the  variations  of  the  barometer  correspond  to  the  va- 
riations in  the  weight  of  the  air  at  the  same  place,  and  since  these 
variations  are  connected  with  changes  of  weather,  this  instrument 
thus  becomes  a  weatherglass,  and  enables  us,  in  certain  cases*  to  fore- 
see changes  of  weather.     The  most  uniform  indications  of  the  ba- 


or  two.  It  must  be  recollected,  that  any  impulse  or  pressure  exerf- 
ed  on  the  surface  of  the  fluid  in  the  vessel,  extends  alike  to  every 
part  of  it;  and  since  fluids  act  upwards  as  well  as  downwards,  it  is 
plain  that  the  pressure  acts  in  sustaining  the  column  of  mercury  in 
the  same  manner  as  though  it  were  applied  directly  to  the  mouth  of 
the  tube. 
*  From  £«£<>£  weight,  and  /j^lpov  measure. 


152  PNEUMATICS. 

rometer  are,  that  its  rise  denotes  fair,  and  its  fall  denotes  foul  weather 
whatever  may  be  its  absolute  height.  Also  a  sudden  and  extraordi- 
nary descent  of  the  mercury  attends,  and  frequently  precedes  a  vio- 
lent wind. 

299.  The  mean  pressure  of  the  atmosphere,  as  indicated  by  the 
barometer,  is  nearly  the  same,  at  the  level  of  the  sea  in  all  parts  of 
the  earth  corresponding  very  nearly  to  30  inches  of  mercury.  This 
fact  has  been  verified  by  numberless  observations,  made  with  the  ba- 
rometer in  both  hemispheres,  from  the  equatorial  to  the  polar  regions. 
The  following  results  for  several  places,  in  different  latitudes,  correct- 
ed for  temperature,  elevation  above  the  level  of  the  sea,  and  the  in- 
fluence of  the  earth's  rotation  on  its  axis,  are  nearly  uniform. 

Latitude.  Bar.  Pressure. 

Calcutta,     -         -         -     22°  35'       -  29.776 

London,  51     31  -  29.827 

Edinburgh,  -     55     56       -  29.835 

Melville  Island,  74     30  -    29.884 

But,  though  the  mean  pressure  of  the  atmosphere  is  nearly  the 
same,  at  the  level  of  the  sea,  over  the  whole  globe,  the  extent  of  the 
variations  to  which  it  is  liable,  is  exceedingly  different  in  different 
parallels  of  latitude.  At  the  equatorial  regions,  the  range  of  the  ba- 
rometer is  much  more  limited  than  within  the  polar  circles ;  and  in 
the  frigid  zones,,  it  is  more  limited  than  in  the  temperate.  Within 
the  tropics  the  fluctuations  of  the  barometer  do  not  much  exceed  J  of 
an  inch,  while  beyond  this  space,  they  reach  to  3  inches.  The  most 
extensive  variations  take  place  between  the  latitudes  of  30°  and  60°, 
being  the  zone  in  which  the  annual  changes  of  temperature  and  hu- 
midity possess  the  widest  range. 

300.  Shortly  after  the  invention  of  the  barometer,  it  was  observed 
that  the  mercury  descends,  when  the  instrument  is  carried  to  a  more 
elevated  situation.  The  descent  is  found  to  be  about  T\  of  an  inch 
for  87  feet.  From  this  observation,  we  may  deduce  the  specific 
gravity  of  air  compared  with  mercury  or  water ;  for  y1^  of  an  inch  of 
mercury  has,  it  appears,  the  same  weight  as  87  feet,  or  1044  inches, 
of  air/  Consequently,  1  inch  of  mercury  weighs  as  much  as  10440 

/ 10440     \ 
inches  of  air;  that  is,  mercury  is  10440  times,  and  water  is  i  13  57  ==) 

769  times,  heavier  than  air. 


ATMOSPHERE.  153 

301.  As  the  air  pump  enables  us  to  investigate  the  mechanical 
properties  of  any  portion  of  air,  so  the  barometer  enables  us  to  study 
the  properties  and  relations  of  the  entire  body  of  the  air,  that  is,  the 
atmosphere.  By  means  of  these  two  instruments,  the  following  facts 
are  well  established. 

( 1 . )  The  space  occupied  by  any  given  portion  of  otr,  (as  1 00  grains 
for  example,)  is  inversely  as  the  pressure.  A  weight  of  two  atmos- 
pheres diminishes  the  bulk  to  one  half;  of  three  atmospheres,  to  one 
third  ;  and  of  one  hundred  atmospheres,  to  one  hundreth  part  of  its 
former  bulk. 

(2.)  As  the  density  is  likewise  inversely  as  the  space  occupied, 
therefore,  the  density  is  as  the  pressure. 

(3.)  Since  air  when  compressed,  endeavors  to  restore  itself,  with 
a  force  which  is  equal  to  that  which  compresses  it,  (being  when  at 
rest  in  equilibrium  with  that  force,)  therefore,  the  elasticity  is  as  the  , 
density  and  inversely  as  the  space  occupied.  In  this  proposition,  the 
temperature  is  supposed  to  remain  uniform.  But,  the  bulk  and  den- 
sity of  a  portion  of  air  remaining  the  same,  the  elasticity  is  as  the 
temperature.  Hence  the  elasticity  of  air  maybe  increased  either 
by  compressing  it,  or  by  heating  it  in  a  confined  state  ;  and  its  elas- 
ticity may  be  diminished  either  by  lessening  the  pressure,  or  by  cool- 
ing it.  The  elasticity  of  springs  is  known  to  be  frequently  impaired 
by  continual  action.  This  is  not  the  case  with  air.  Air  has  been 
left  for  several  years  very  much  compressed  in  suitable  vessels,  in 
which  there  was  nothing  that  could  have  a  chemical  action  upon  it ; 
and  afterwards,  on  removing  the  unusual  pressure,  and  restoring  the 
same  temperature,  the  air  has  been  found  to  recover  its  original  bulk 
which  shows  that  the  continuance  of  the  pressure  had  not  diminished 
the  elasticity  of  it  in  the  least  perceptible  degree. 


CHAPTER  II. 

OF  THE  ATMOSPHERE. 

302.  The  knowledge  now  acquired  of  the  properties  of  elastic' 
fluids,  will  qualify  the  learner  to  enter  advantageously  upon  the  study 
of  the  entire  body  of  the  air,  which  constitutes  the  atmosphere, 

20 


154  PNEUMATICS. 

Let  us  therefore  now  proceed  to  consider  its  weight, — its  extent  and 
density, — its  relations  to  heat  and  moisture,  giving  rise  to  the  various 
phenomena  of  Meteorology, — and  its  relations  to  sound,  whence 
arises  the  science  of  Acoustics. 

303.  The  WEIGHT  of  the  entire  atmosphere  may  be  easily  esti- 
mated by  means  of  the  barometer  ;  for  taking  the.  medium  height  of 
the  mercury  at  thirty  inches,  the  weight  of  the  atmosphere  is  equal 
to  that  of  a  sea  of  quicksilver,  covering  the  whole  earth  to  the  depth 
of  two  and  a  half'feet.     This  would  add  five  feet  to  the  diameter 
of  the  globe,  and  the  contents  of  the  whole  mass  of  quicksilver,  in 
cubic  feet,  would  be  equal  to  the  difference  between  the  solid  con- 
tents of  the  globe,  and  those  of  a  sphere  of  a  diameter  five  feet  great- 
er.    Having  the  number  of  cubic  feet  of  quicksilver, 'we  have  only 
to  multiply  that  number  by  the  weight  of  one  foot,   and  we  obtain, 
for  the  weight  of  the  whole  atmosphere,  11,624914,803603,492864 
Ibs.,  or  more  than  eleven  trillions  of  pounds,  or  five  thousand  billions 
of  tons. 

304.  Were  the  atmosphere  of  equal  density  throughout,  it  would 
be  easy  to  determine  its  height,  since  opposite  columns  of  different 
fluids  are  in  equilibrium,  when  their  heights  are  inversely  as  their 
specific  gravities,  (Art.  251.)     Therefore,  as  the  specific  gravity  of 
air  is  to  that  of  quicksilver,  so  is  the  height  of  the  column  of  quick- 
silver to  the  corresponding  height  of  the  column  of  air  that  balances 
it.     That  is,  1  :  10440:  :2.5  :  26100  feet=5  miles  nearly. 

But  the  atmosphere  is  very  far  from  being  throughout  of  uniform 
density.  Several  causes  conspire  to  produce  this  result.  1.  The 
different  quantities  of  superincumbent  air  at  different  altitudes;  2. 
The  decreasing  attraction  of  the  earth  in  proportion  as  the  square  of 
the  distance  from  its  center  increases  ;  3.  The  influence  of  heat  and 
cold;  4.  The  admixtures  of  vapors  and  other  fluids ;  5.  The  attrac- 
tion of  the  moon  and  other  celestial  bodies.  That  the  lower  strata 
of  the  atmosphere  are  far  more  dense  than  the  upper,  will  be  obvious 
from  this  consideration,  that  the  portions  which  rest  on  the  surface  of 
the  ear,th,  sustain  the  weight  of  the  whole  body  of  the  atmosphere, 
which,  as  appears  from  Ail.  303,  is  immensely  great.  But  the  den- 
sity of  air  is  as  the  compressing  force.  (Art.  301.)  As  we  ascend 
from  the  earth,  the  weight  sustained  is  constantly  diminished,  and  the 
density  lessened,  according  to  the  following  law. 


ATMOSPHERE.  155 

305.  The  densities  of  the  air  decrease  in  a  geometrical,  as  the 
distances  from  the  earth  increase  in  an  arithmetical  ratio. 

306.  By  observations  on  the  barometer  at  different  altitudes,  aid- 
ed by  calculation,  it  is  ascertained,  that  at  the  height  of  seven  miles 
above  the  earth,  the  air  is  only  one  fourth  as  dense  as  it  is  at  the 
surface.     Hence  if  we  take  an  arithmetical  series,  increasing  by 
seven,  to  denote  different  heights,   and  a  geometrical  series  whose 
constant  multiplier  is  one  fourth,  to  denote  the  corresponding  densi- 
ties, we  may  easily  ascertain  the  density  of  the  air  at  any  proposed 
elevation. 

Arithmetical  series,  7  14  21  28  35  42  49 
Geometrical  series,  {  TV  T'T  ¥}g-  „'„  ToVe  TFFTI 
From  this  table  it  appears,  that  at  the  height  of  twenty  one  miles, 
the  air  is  sixty  four  times  as  rare  as  at  the  surface  of  the  earth ;  at 
the  height  of  forty  nine  miles,  sixteen  thousand  three  hundred  and 
eighty  four  times  as  rare ;  and  if  we  pursue  the  calculation,  we  shall 
find  that  its  rarity  at  the  moderate  distance  of  only  one  hundred  miles, 
is  one  thousand  millions  of  times  greater  than  at  the  earth,  and  of 
course  would  oppose  no  sensible  resistance  to  bodies  revolving  in  it. 
De  Luc  ascended  in  a  balloon  to  such  a  height  that  his  barometer  fell 
to  twelve  inches.  Supposing  the  barometer  at  the  surface  to  have 
stood,  at  that  time,  at  thirty  inches,  it  follows  that  he  must  have  left 
three  fifths  of  the  whole  atmosphere  below  him ;  for  six  inches  being 
one  fifth  of  thirty,  twelve  inches  must  be  two  fifths,  and  consequently 
three  fifths  of  the  whole  must  be  below.  His  elevation  was  upwards 
of  twenty  thousand  feet. 

If  there  were  an  opening  into  the  interior  of  the  earth,  which  would 
permit  the  air  to  descend,  its  density  would  increase  in  the  same 
manner  as  it  diminishes  in  the  opposite  direction.  At  the  depth  of 
about  thirty  four  miles,  it  would  be  as  dense  as  water ;  at  the  depth 
of  forty  eight  miles,  it  would  be  as  dense  as  quicksilver ;  and  at  the 
depth  of  about  fifty  miles,  as  dense  as  gold. 

307.  The  foregoing  law,  however,  does  not  afford  exact  data  for 
estimating  the  density  of  the  air  at  any  given  elevation,  since  the  den- 
sity is  affected  by  the  several  other  circumstances  mentioned  in  arti- 
cle 304,  which  are  not  here  taken  into  the  account.     Since  the  force 
of  attraction  diminishes  as  the  square  of  the  distance  from  the  center 
of  the  earth  increases,  this  diminution  will  occasion  a  corresponding 


156  PNEUMATICS. 

decrease  of  density.  However,  as  the  force  of  attraction  will  be 
very  nearly  the  same  at  such  elevations  as  the  highest  mountains,  as 
at  the  general  level  of  the  earth,  no  allowance  is  made  on  this  account 
for  barometric  measurements,  except  in  cases  when  extreme  accu- 
racy is  required.  Changes  of  temperature  produce  a  much  greater 
effect,  since  heat  expands  and  cold  contracts  the  air ;  and  therefore, 
in  estimating  altitudes,  the  state  of  the  thermometer  is  always  to  be 
taken  into  account,  in  connexion  with  the  height  of  barometer. 
Heat  and  cold  also  affect  the  height  of  the  mercury  in  the  barometer, 
independently  of  the  pressure  of  the  atmosphere  without,  and  there- 
fore it  becomes  necessary  to  reduce  the  observations  to  a  fixed 
{standard  of  temperature. 

308.  As  we  ascend  from  the  earth,  the  temperature  of  the  air 
constantly  diminishes  until  we  arrive  at  a  region  of  frost,  the  lower 
limit*of  which  is  called  the  term  of  perpetual  congelation.  The 
heights  of  the  term  of  congelation  for  every  parallel  of  latitude  from 
the  equator  to  the  north  pole,  have  been  computed,  partly  from  ob- 
servation, and  partly  from  the  known  mean  temperature  of  each  par- 
allel, and  the  decrement  of  heat  as  we  ascend  in  the  atmosphere  ; 
and  the  result  is  expressed  in  the  following  table  : — 

Latitude.  Mean  height  of  the  term  Differences  for  every 

of  congelation  in  feet.  5  deg.  of  latitude. 

0  '  15577 

5  15455  -     122 

10  .  15067  388 

15  14498  569 

20  13719  ^     779 

25  -         13030     -    -  689 

30  11592  1438 

35  10664  928 

40  9016  1648 

45  7658  1358 

50  6260  1398 

55  4912  1348 

6p  3684  1238 

65*  2516  1168 

70  1557  959 

75  748  809 

80  -    -       120  628 


ATMOSPHERE.  157 

From  this  table  it  appears,  that  the  height  of  the  region  of  per- 
petual frost  at  the  equator  is  almost  three  miles ;  at  the  parallel 
of  35°,  about  two  miles ;  and  at  the  latitude  of  54°,  about  one  mile; 
while  at  the  latitude  of  80°,  this  region  approaches  very  near  to  the 
earth,  and  at  the  pole  it  probably  comes  nearly  or  quite  down  to 
the  earth.  It  is  farther  to  be  remarked,  that  the  different  heights 
decrease  very  slowly  as  we  recede  from  the  equator,  until  we  reach 
the  limits  of  the  torrid  zone,  when  they  decrease  much  more  rapidly 
the  maximum  being  at  the  parallel  of  40°.  The  average  difference 
for  every  five  degrees  of  latitude  from  30°  to  60°,  is  1334,  while 
from  the  equator  to  30°,  the  average  is  only  509,  and  from  60°  to 
80°,  it  is  only  891.  Important  meteorological  phenomena  depend 
on  this  fact. 

309.  As  a  portion  of  air  rarefied  by  heat  at  the  earth's  surface 
ascends,  the  diminishing  pressure  which  it  sustains  as  it  rises,  has  a 
tendency  to  enlarge  its  volume.     But  on  the  other  hand,  an  enlarge- 
ment of  volume,  increases  its  capacity  for  heat,  and  lowers  its  temper- 
ature, which  tends  to  condense  it.     At  a  moderate  elevation  above 
the  earth,  these  causes  operate  to  keep  the  air  at  rest  and  thus  the 
heat  of  the  earth  is  incapable  of  raising  the  temperature  of  the  air, 
except  within  a  moderate  distance,  beyond  which  the  region  of  frost 
pervails,  and  the  cold  continues  to  increase,  until  it  probably  reaches 
at  a  comparatively  moderate  distance  from  the  earth,  an  intensity  al- 
most inconceivable. 

Relations  of  Mr  to  Heat. 

310.  Air  is  set  in  motion  by  every  cause  which  disturbs  its  equili- 
brium.    It  is  more  sensible  than  the  most  delicate  balance,  and'moves 
with  the  slightest  inequalities  of  pressure. 

Air  is  put  in  motion  by  'the  least  change  of  temperature.  Heat 
rarefies  it,  and  renders  it  specifically  lighter  than  the  neighboring  por- 
tions, and  it  ascends,  while  colder  and  denser  portions  flow  in  to  re- 
store the  equilibrium.  On  the  other  hand,  if  air  be  condensed  by 
cold,  it  descends,  or  flows  off,  until  it  meets  with  air  of  the  same 
density,  where  it  rests.  These  effects  naturally  result  from  the  per- 
fect fluidity  and  elasticity  of  this  substance. 


158 


PNEUMATICS. 


Fig.  72. 


311.  An  illustration  of  this  principle  is  seen  in  the  manner  in  which 
air  circulates  in  the  shaft  or  pit  of  a  deep  mine.  Such  a  circulation 
is  kept  up  briskly,  even  amounting  sometimes  to  a  strong  wind, 
when  two  shafts  or  pits  of  unequal  heights  are  made  to  communi- 
cate with  each  other  by  means  of  a  horizontal  gallery,  called  a  drift. 
The  earth  remains  nearly  at  the  same  temperature  summer  and 
winter,  while  the  external  air  is  hotter  in  summer  and  colder  in  win- 
ter, than  that  within  the  mine.  Now  were  the  air  within  the  earth 
and  without,  of  the  same  density  then 
the  air  of  the  two  shafts  and  of  the 
drift  would  remain  in  equilibrio,  the 
longer  shaft  A,  being  counterbalanced 
by  the  shorter  shaft  B,  extending  so 
as  to  embrace  C,  a  portion  of  the  ex- 
ternal air,  to  the  same  height  as  the 
column  A.  But  suppose  it  summer ; 
then  the  air  in  A,  becoming  condensed 
by  the  influence  of  the  colder  earth, 
*s  rendered  specifically  heavier,  and  . 
overpowers  in  the  columns  B  and  C, 
the  latter  consisting  of  air  more  rarefi- 
ed than  that  within  the  earth.  Hence 
the  air  will  flow  down  the  longer,  and 
out  of  the  shorter  shaft ;  and  by  bring- 
ing all  parts  of  the  mine  into  the  cir- 
culation the  whole  interior  will  be  ventilated.  Again,  suppose  it  win- 
ter ;  then  the  air  in  the  longer  shaft  being  warmer  and  more  rarefied 
than  the  compound  column  BC,  the  latter  preponderates,  and  the  air 
flows  in  the  opposite  direction  ;  namely,  down  the  shorter  and  out 
at  the  longer  shaft.  In  spring  and  autumn,  when  the  temperature  of 
the  atmosphere  and  the  mine  are  nearly  equal,  the  miners  complain 
much  of  the  suffocating  state  of  the  air. 

.  312.  The  contemplation  of  the  motions  of  the  atmosphere  on  a 
large  scale,  as  they  exist  in  nature,  leads  to  the  subject  of  Winds ; 
but  we.  may  see  the  same  principles  exemplified  in  chimnies  and  fire- 
places. A  chimney  may  be  regarded  as  a  perpendicular  tube,  con- 
taining a  column  of  air.  Since  the  density  of  the  air  is  less  above 
than  below,  and  consequently  the  resistance  less  at  the  top  than  at 


Hor.  drift. 


ATMOSPHERE. 


159 


the  bottom  of  the  chimney,  the  tendency  of  any  current  of  air  through 
the  tube  is  upward,  flowing  in  the  direction  in  which  the  resistance 
is  least.  When  the  air  of  the  chimney  is  rarefied  by  heat  from  the 
fire-place,  the  cold  air  from  below  makes  its  passage  upwards  into 
the  partial  void,  and  thus  supplies  air  to  the  fire  to  support  its  com- 
bustion, and  carries  up  along  with  it  the  smoke  and  vapors  which 
proceed  from  the  fire.  The  smoke,  it  will  be  remarked,  is  carried 
up,  mechanically,  by  the  ascending  current  of  hot  air;  for  smoke  is 
itself  heavier  than  air,  and  sinks  or  descends  when  not  thus  support- 
ed.* The  draught  of  the  chimney,  or  the  strength  and  velocity 
of  the  ascending  current,  is  influenced  by  several  circumstances. 
(1.)  Long  chimnies  have  a  stronger  draught  than  short  ones,  be- 
cause they  present  a  longer  column  of  rarefied  air ;  but  they  may 
be  so  long  as  to  cool  the  air  too  much  before  it  has  reached  the 
top,  in  which  case  the  smoke  falls  by  its  greater  specific  gravity. 
Long  horizontal  pipes,  connected  with  fire-places  or  stoves,  are  apt 
to  smoke,  for  a  similar  reason.  (2.)  A  narrow  throat,  opening  into 
a  large  pipe  or  funnel,  makes  a  strong  draught,  because  the  velocity 
of  the  ascending  current  is  thus  increased,  it  being  in  different  parts 
of  the  chimney  inversely  as  the  area  of  the  section.  The  throat  of 
the  chimney,  however,  must  be  wide  enough  to  admit  freely  all  the 
mixed  products  of  the  ascending  current,  including  the  rarefied  air, 
smoke,  watery  vapor,  and  so  on;  and,  consequently,  a  wider  throat 
is  required  for  green  wood  than  for  dry,  and  least  of  all  for  anthra- 
cite coal,  where  the  amount  of  volatile  substances  expelled  from  the 
fuel  is  comparatively  small.  (3.)  A  fire-place  with  a  low  front  or 
breast,  has  a  strong  draught,  because,  in  this  case,  no  air  can  enter 
the  chimney,  except  such  as  has  felt  the  influence  of  the  fire,  and 
is  thus  fitted  to  keep  the  chimney  warm ;  whereas,  if  the  throat  of 
the  fire-place  is  high,  much  of  the  air  that  flows  into  it  is  cold  and 
cools  the  chimney,  and  of  course  diminishes  the  degree  of  rarefac- 
tion in  it.  Moreover,  when  the  throat  is  near  the  fire,  it  becomes 


*  This  fact  is  illustrated  by  an  experiment,  suggested  by  Dr.  Frank- 
lin, viz.  by  blowing  the  smoke  of  a  tobacco  pipe  through  water  in  a 
tumbler.  The  smoker  being  cooled  by  this  process,  rests  upon  the 
surface  of  the  water. 


160  PNEUMATICS. 

more  intensely  heated,  and  thus  the  degree  of  rarefaction  of  the  cur- 
rent of  air  that  passes  through  it  is  augmented  and  its  velocity  in- 
cr.eased.  In  the  structure  of  fire-places  and  stoves,  it  is  an  impor- 
tant principle,  that  as  little  air  as  possible  should  get  into  the  flue  of 
the  chimney,  except  what  passes  through  the  fire  ;  and  it  is  another 
important  principle,  in  regard  to  the  economy  of  fuel,  that  no  more 
air  should  traverse  the  fire  than  what  is  necessary  to  support  the 
combustion.  All  the  air  that  passes  through  the  fire,  over  and  above 
what  undergoes  decomposition,  cools  it,  and  carries  a  portion  of  the 
heat  up  chimney.  It  is  obvious  that  the  air  of  an  apartment  must 
be  denser  than  that  at  the  top  of  the  chimney,  otherwise  the  current 
will  flow  downwards,  as  is  sometimes  the  case  when  the  room  is  very 
close,  and  the  throat  of  the  fire-place  so  large  as  to  require  a  great 
quantity  of  air  to  fill  the  rarefied  space,  in  which  case,  the  air  of  the 
room  is  speedily  exhausted.  Hence,  the  advantage,  in  close  apart- 
ments, of  small  fire-places,  or  stoves  which  require  but  a  small  sup- 
ply of  air. 

313.  But  a  much  more  extensive  operation  of  the  same  principles 
is  exhibited  to  us  by  nature,  in  the  phenomena  of  WINDS.     Rarefac- 
tion by  heat  and  condensation  by  cold  are  the  chief  causes  of  winds. 
Their  distinct  existence  and  modes  of  operation,  can  frequently  be 
discovered  ;•  and,  in  cases  where  we  can  discover  neither,  we  are  au- 
thorized to  infer  the  presence  of  such  a  cause,  since  it  is  so  constant- 
•  ly  connected  with  the  same  effects  in  very  numerous  examples  that 
daily  pass  before  our  eyes,  while  we  are  unacquainted  with  any  other 
adequate  causes  of  the  same  phenomena.     The  motion  of  the  air, 
however,  producing  a  wind,  may  be  merely  relative,  arising  from  the 
motion  of  the  spectator.     Thus  a  steam  boat,  moving  at  the  rate  of 
sixteen  miles  an  hour  in  a  perfect  calm,  would  appear  to  one  on  board 
to  be  facing  a  wind,  moving  at  the  same  rate  in  the  opposite  direc- 
tion ;  or  if,  in  the  diurnal  revolution  of  the  earth  on  its  axis,  any 
point  of  the  earth's  surface  should  move  faster  than  the  portion  of 
the  atmosphere  above  it,  a  relative  wind  in  the  opposite  direction 
would  ,be  the  result.     The  direction  of  the  wind  may  be  modified 
by  various  causes,  the  actual  direction  being  the  resultant  of  two  or 
more  currents  which  meet  from  different  directions,  or  of  several  dif- 
ferent forces. 


ATMOSPHERE, 


161 


314.  Land  and  sea  breezes  afford  a  striking  exemplification  of  the 
principle  in  question.     These  winds  prevail  in  most  maritime  coun- 
tries, but  more  especially  in  the  islands  of  the  torrid  zone,  blowing 
off  from  the  land  at  night,  and  towards  the  land  in  the  day  time.     If 
we  place  a  hot  stone  in  a  room,   (says  Dr.  Robison,)  and  hold  near 
to  it  a  candle  just  extinguished,  we  shall  see  the  srtioke  move  towards 
the  stone,  and  then  ascend  up  from  it.     Now,  suppose  an  island  re- 
ceiving the  first  rays  of  the  sun  in  a  perfectly  calm  morning ;  the 
ground  will  become  warm,  and  will  rarefy  the  contiguous  air.     If  the 
island  be  mountainous,  this  effect  will  be  more  remarkable ;  because 
the  inclined  sides  of  the  hills  will  receive  the  heat  more  directly. 
The  midland  air  will  therefore  be  most  warmed ;  the  heated  air  will 
rise,  and  that  in  the  middle  will  rise  fastest ;  and  thus  a  current  of 
air  upwards  will  begin,  which  must  be  supplied  by  air  coming  in  on 
all  sides,  to  be  heated  and  to  rise  in  its  turn  ;  and  thus  the  morning 
sea  breeze  is  produced,   and  continues  all  day.     This  current  will 
frequently  be  reversed  during  the  night,  by  the  air  cooling  and  gli- 
ding down  the  sides  of  the  hills,  and  we  shall  then  have  the  land 
breeze. 

315.  The  trade  winds  afford  an  example  of  the  operation  of  the 
same  causes  on  a  still  greater  scale.     These  winds  prevail  in  the  tor- 
rid zone  and  a  little  beyond  it,  extending  to  nearly  30°  on  both  sides 
of  the  equator.     When  not  affected  by  local  causes,  they  blow  con^ 
stantly  at  the  same  place,  in  one  and  the  same  direction,  throughout 
the  year.     Their  general  direction  is  from  north-east  to  south-west 
on  the  north  side  of  the  equator,  and  from  south-east  to  north-west 
on  the  south  side  of  the  equator.     They  owe  their  origin  to  the  com- 
bined agency  of  two  causes,  namely,  the  movement  of  the  air  on  ei- 
ther side  01  the  equator,  northward  or  southward  towards  the  place  of 
greatest  rarefaction,  and  the  westerly  tendency  arising  from  the  effect 
of  the  earth's  diurnal  rotation  on  its  axis,  since  they  do  not  instan- 
taneously acquire  the  greater  velocity  which  the  equatorial  regions 
have,  in  consequence  of  the  earth's  revolution  oti  its  axis.    The  dura- 
tion of  the  trade  winds  is  variously  modified  in  different  parts  of  the 
world,  but  always  in  such  a  manner,  that  they  blow  towards  the  point 
of  greatest  rarefaction,   and  receive  a  relative  motion  from  the  effect 
of  the  earth's  diurnal  rotation. 

21 


162  PNEUMATICS. 

Relations  of  Mr  to  Moisture. 

316.  The  foregoing  atmospheric  phenomena  arise  chiefly  from 
the  relations  of  air  to  Heat;  we  are  next  to  trace  a  few  of  the  lead- 
ing phenomena,  which  result  from  the  relations  of  air  to  Moisture. 

By  the  action  of  the  sun's  heat  upon  the  surface  of  the  earth, 
whether  land  or  water,  immense  quantities  of  vapor  are  raised  into 
the  atmosphere,  supplying  materials  for  all  the  water  that  is  deposited 
again  in  the  various  forms  of  dew,  fog,  rain,  snow,  and  hail.  Our 
limits  will  now  allow  us  to  enter  largely  into  Meteorology,  under  which 
head  the  various  phenomena  of  the  atmosphere  are  included,  but 
we  shall  be  able  barely  to  glance  at  the  subject. 

317.  The  leading  principle  upon  which  the  precipitaton  of  moist- 
ure from  the  atmosphere,  under  any  form,  depends,   is  the  follow- 
ing : — 

The  capacity*  of  air  for  moisture  is  increased  by  heat  and  dimin- 
ished by  cold. 

In  other  words,  air  by  being  heated  is  rendered  capable  of  taking 
up  and  holding  a  greater  quantity  of  water  in  the  invisible  state,  and 
by  being  cooled,  its  power  of  thus  holding  water  is  lessened. 

Again,  the  capacity  of  air  for  moisture  increases  faster  than  the 
temperature;  so  that  the  addition  of  ten  degrees  of  heat  to  air  already 
at  the  temperature  of  70°,  will  increase  the  capacity  for  water  much 
more  than  the  same  addition  would  do  when  made  to  air  at  the  tem- 
perature of  40°.  On  the  other  hand,  the  cooling  of  hot  air  dimin- 
ishes its  capacity  for  moisture  much  faster  than  the  cooling  of  air 
already  cold. 

*  The  term  capacity  being  frequently  employed  in  the  physical  sci- 
ences, it  is  important  for  the  student  to  obtain  clear  and  correct  views 
of  its  meaning.  The  power  of  a  sponge  to  hold  water,  to  stow  it 
away  in  the  interior,  so  as  to  render  it  invisible,  is  the  capacity  of  the 
sponge  for  water.  This  capacity  is  capable  of  increase  or  diminution. 
Take  a  piece  of  dry  sponge,,  and  soak  it  in  water;  as  its  volume  en- 
larges, its  capacity  for  water  increases — remove  it  from  the  water,  and 
squeeze  it  gently ;  a  part  of  the  water  runs  out — suffer  it  to  expand 
and  it  appears  nearly  dry;  squeeze  it  again,  and  it  becomes  wet. 
Hence  we  say  its  capacity  is  increased  by  an  enlargement  of  volume, 
and  diminished  by  compression. 


ATMOSPHERE.  163 

318.  DEW  is  formed  when  the  air  comes  in  contact  with  a  sur- 
face in  a  certain  degree  colder  than  itself.  This  is  the  simplest  de- 
position of  moisture  from  the  atmosphere.  Thus  dew  is  formed 
copiously  on  a  cup  of  cold  water  during  summer,  particularly  be- 
fore a  thunder  shower ;  because  then  the  air  is  hot,  and  saturated 
with  moisture,  a  portion  of  which  it  deposits  as  soon  as  it  is  cooled, 
its  capacity  for  moisture  being  thus  diminished.  It  is  ascertained  by 
actual  observation  that  on  those  nights  when  copious  dews  occur,  the 
ground  becomes  twelve  or  fourteen  degrees  colder  than  the  air  a  few 
feet  above  it.  Consequently  whenever  the  air,  by  circulating  over 
the  surface  of  the  ground,  comes  in  contact  with  this  colder  surface, 
it  deposits  a  portion  of  moisture  upon  it.  The  quantity  actually  de- 
posited will  of  course  be  greater  as  the  difference  of  temperatures 
between  the  air  and  the  ground  is  greater,  and  the  air  is  more  nearly 
saturated  with  moisture. 

Dew  is  found  to  be  deposited  on  different  substances  unequally, — 
more  on  vegetables  than  on  drysand;  very  little  on  bright  metallic 
surfaces ;  and  none  at  all  on  large  bodies  of  water,  as  the  ocean.  In 
all  cases,  however,  these  surfaces  are  observed  to  maintain  a  corre- 
sponding difference  in  the  temperature  they  acquire,  some  growing 
much  colder  than  others  equally  exposed,  while  the  surface  of  the 
ocean  remains  at  the  same  temperature  as  the  air  incumbent  on  it. 
The  air  therefore  sustains  no  reduction  of  capacity  by  circulating 
upon  it,  and  no  dew  is  deposited. 

319.  FOGS  are  produced  by  watery  vapor  coming  in  contact  with 
air  colder  than  itself. 

The  vapor  may  be  such  as  is  just  rising  from  the  ground,  or  such 
as  before  existed  in  a  body  of  common  air  that  meets  and  mixes  with 
the  colder  air.  Thus,  in  a  cold  morning,  smoke  proceeds  from  va- 
rious moist  substances,  as  from  the  breath  of  animals,  from  a  hole  in 
the  ice  of  a  river,  from  wells,  and  from  many  other  sources.  In  each 
case,  the  vapor  meets  with  cold  air,  which  having  so  small  a  capacity 
for  moisture,  is  unable  to  hold  it  in  solution,  and  it  is  deposited  in  the 
form  of  fog.  A  striking  example  of  fogs  is  seen  over  rivers,  partic- 
ularly in  a  summer  morning,  marking  out  their  courses  for  a  great 
distance.  Here,  since  the  temperature  of  the  water  changes  but  lit- 
tle during  the  night,  while  the  neighboring  land,  and  of  course  the  air 


164  PNEUMATICS. 

0 

over  the  land,  has  become  cold,  the  vapor  which  rises  from  the  river 
during  the  night,  and  meets  with  cold  air,  is  condensed  into  a  fog. 
The  fogs  formed  over  shoals  and  sand  banks,  as  the  banks  of  New- 
foundland, are  deposited,  from  the  warm  and  humid  air  of  the 
ocean,  which  is  cooled  by  mixing  with  the  cold  air  over  the  banks. 
Fogs  are  phenomena  of  cold  climates,  and  are  not  so  common  in  hot 
countries ;  the  air  in  such  situations  having  too  great  a  capacity  for 
moisture,  to  permit  it  to  condense  into  a  fog  near  the  surface  of  the 
earth. 

320.  CLOUDS  are  dependent  on  the  same  principle  as  fogs,  consist- 
ing of  vapor  condensed  by  the  cold  of  the  upper  regions.     They  are 
formed  over  water,  or  moist  places,   by  vapor  rising  so  high,  as  to 
reach  a  degree  of  cold  sufficient  to  condense  it ;  or  they  result  from 
the  mixture  of  warmer  with  colder  air,  proceeding  always  from  the 
warmer  portion. 

321.  RAIN  is  produced  by  the  sudden  cooling  of  air,  charged  with 
large  quantities  of  watery  vapor. 

Suppose  two  bodies  of  air,  a  hotter  and  a  colder  portion,  both  sat- 
urated with  moisture,  to  meet ;  the  compound  would  assume  a  tem- 
perature which  was  the  mean  between  the  two ;  but  the  quantity  of 
heat  which  the  colder  portion  of  air  would  gain,  would  not  increase 
its  capacity  so  much  as  that  of  the  warmer  body  would  be  diminish- 
ed, by  the  loss  of  the  same  portion  of  heat.  (Art.  317.)  Hence  the 
capacity  of  the  mixture  would  be  less^han  the  average  capacities  of 
the  separate  portions,  and  consequently  water  would  be  deposited. 
If  the  separate  portions  of  air  are  not  completely  saturated  with  mois- 
ture, still  the  capacity  of  the  mixture  may  be  so  much  less  than  that 
of  the  constituents,  as  to  render  it  unable  to  hold  all  the  water  they 
contained ;  and  in  this  case,  more  or  less  water  would  be  deposited. 

322.  This  view  of  the  general  cause  of  rain,  (which  is  commonly 
called  Button's  Theory  of  Rain,  from  Dr.  Hutton,  of  Edinburg,  who 
first  pjaoposed  it,)  is  capable  of  being  confirmed  by  an  extensive  in- 
duction of  facts,  by  which  it  would  appear,  that  variable  winds,  fa- 
vorable to  the  mixture  of  air  of  different  temperatures,  are  accompa- 
nied by  rain,  while  constant  winds  are  accompanied  by  dry  weather. 


MECHANICAL  AGENCIES  OF  AIR.  165 

323.  HAIL  is  produced  by  the  mixture  of  exceedingly  cold  air, 
with  a  body  of  hot  and  humid  air.  The  cold  wind  is  supposed  to 
be  derived  from  an  elevation  considerably  above  the  term  of  perpet- 
ual congelation,  and  to  be  suddenly  transferred  to  a  body  of  hot  and 
humid  air,  from  which  it  preciptates  the  hail.  Or  it  may  be  suppos- 
ed to  result  from  a  hot  wind  blowing  from  the  torrid  regions  into  the 
limits  of  perpetual  frost,  and  thus  having  its  watery  vapor  suddenly 
congealed.  Or  it  may  be  the  product  of  the  meeting  of  a  very  cold 
with  a  very  hot  wind.  All  that  the  theory  requires,  in  order  that  hail 
should  be  precipitated,  is,  that  very  hot  and  very  cold  bodies  of  air 
should  be  mixed  in  any  way  whatsoever.  Accordingly,  hail  is  found 
to  be  most  frequent  and  violent  in  those  regions  where  hot  and  cold 
bodies  of  air  are  most  easily  mixed.  Such  mixtures  are  rarely 
formed  in  the  torrid  zone,  since  there  the  portion  of  cold  air  would 
be  wanting;  and  a  similar  difficulty  exists  in  the  frigid  zone,  for  there 
the  hot  air  is  wanting ;  but  in  the  temperate  climate,  the  heated  air 
of  the  south,  and  the  intensely  cold  winds  of  the  north,  may  be  much 
more  easily  brought  together ;  and,  accordingly,  in  the  temperate 
zones  it  is,  that  hail  storms  chiefly  occur.  Even  in  these  climates 
they  are  most  frequently  found  in  places,  where  such  mixtures  are 
most  easily  formed,  as  in  the  south  of  France,  lying,  as  it  does,  be- 
tween the  Pyrenees  and  the  Alps,  which  are  covered  with  perpetu- 
al snows,  while  the  intervening  country  is  ^subject  to  become  highly 
heated  by  the  summer's  sun,  or  is  even  visited,  especially  at  a  certain 
elevation,  by  occasional  blasts  of  the  hot  winds  that  cross  the  Medi- 
terranean. 


CHAPTER  III. 

OF  THE  MECHANICAL  AGENCIES  OF  AIR  AND  STEAM. 

324.  In  consequence  of  our  power  of  forming  a  vacuum,  either 
by  the  exhaustion  of  air  or  by  the  condensation  of  steam,  and  of  di- 
recting the  force  with  which  these  elastic  substances  rush  into  a  void 
or  press  towards  it,  air  and  steam  become  important  agents  or  prime 
movers,  in  various  kinds  of  machinery.  Many  of  the  most  useful 
machines  involve  in  their  construction  the  principles  of  both  hydrau- 
lics and  pneumatics,  and  therefore  we  have  reserved  an  account  of 
such  machines  to  the  present  section. 


166  PNEUMATICS. 

The  Syphon. 

325.  If  a  tube  having  two  arms,  a  longer 
and  a  shorter,  be  filled  with  water,  and  the 
mouth  of  the  shorter  arm  be  immersed  in  wa- 
ter, the  fluid  will  run  out  through  dlthe  longer 
arm  until  the  whole  contents  of  the  vessel  are 
discharged.  Such  a  tube  is  called  a  syphon. 
It  may  be  filled  with  the  fluid,  either  by  suction 
or  by  pouring  water  into  it,  keeping  the  two 
orifices  closed  until  the  shorter  arm  is  immer- 
sed, Or,  when  the  syphon  is  large,  each  orifice  is  plugged,  and 
water  is  poured  in  through  an  opening  in  the  top  of  the  bend.  The 
opening  being  closed,  the  shorter  leg  is  placed  in  the  cistern,  and 
the  plugs  removed,  the  fluid  is  discharged  as  usual.  The  principle 
of  the  syphon  is  as  follows.  The  atmosphere  presses  equally  on  the 
mouths  of  both  arms  of  the  tube ;  but  this  pressure  on  each  orifice 
is  diminished  by  the  weight  of  the  column  of  water  in  the  leg  nearest 
to  it;  consequently,  more  of  the  atmospheric  pressure  is  overcome 
by  the  longer  than  by  the  shorter  column,  and  therefore  the  effective 
pressure,  (or  what  remains,)  is  less  at  the  mouth  of  the  longer  than 
at  that  of  the  shorter  column,  and  the  fluid  runs  in  that  direction  in 
which  the  resistance  is  least.  All  this  will  be  obvious  by  inspecting 
the  figure. 

Were  the  shorter  column  thirty  four  feet  in  height,  it  would  coun- 
terbalance the  entire  pressure  of  the  atmosphere  on  the  surface  of 
the  fluid,  and  consequently,  there  would  be  no  force  remaining  to  drive 
the  water  forward  through  the  tube.  The  syphon,  therefore,  can  never 
raise  water  to  a  greater  height  than  thirty  four  feet,  nor  quicksilver  high- 
er than  about  thirty  inches.  It  is  obvious,  also,  that  the  place  of  deliv- 
ery, that  is,  the  mouth  of  the  longer  arm,  must  be  at  a  lower  level 
than  the  surface  of  the  water  in  the  reservoir ;  so  that  this  instru- 
ment cannot  be  used  for  elevating,  but  only  for  decanting  fluids,  or 
transferring  them  from  one  vessel  to  another.  Its  chief  use  is  by 
grocers,  in  transferring  liquors  from  one  cask  to  another.  It  is  some- 
times, employed  in  carrying  water  over  a  hill,  or  from  a  well  to  a 
level  below  the  surface  of  the  well. 


MECHANICAL    AGENCIES    OF    AIR. 


1C7 


Fig.  74. 


B 


II 


The  Common  Suction  Pump. 

326.  This  pump  consists  of  two  hollow  cylinders, 
placed  one  under  the  other,  and  communicating  by  a 
valve  which  opens  upwards.  The  lower  cylinder 
(which  has  its  lower  orifice  under  water)  is  called  the 
suction  tube.  In  the  upper  cylinder,  a  piston  moves 
up  and  down  from  the  bottom  to  a  spout  in  the  side 
near  the  top.  This  cylinder  we  call  the  exhausting 
tube.  Suppose,  at  the  commencement  of  the  opera- 
tion, the  piston  is  at  the  bottom  of  the  exhausting  tube 
in  close  contact  with  the  valve.  On  raising  it,  the  air 
in  the  suction  tube  having  nothing  to  resist  its  upward 
pressure,  lifts  the  valve  and  expands,  so  as  to  fill  the 
void  space  which  would  otherwise  be  left  in  the  lower 
part  of  the  exhausting  tube.  By  this  means,  the  air 
in  the  suction  tube  is  rarefied,  and  no  longer  being  a 
counterpoise  to  the  pressure  of  the  atmosphere  on  the 
surface  of  the  well,  the  latter  predominates  and  forces 
the  water  up  the  tube  until  enough  has  been  raised  ex- 
actly to  counterbalance  the  excess  of  the  elasticity  of 
the  external  air  above  that  of  the  tube.  As  the  piston 
descends,  the  air  below  it  is  prevented  from  returning  into  the  suc- 
tion pipe  by  the  valve  which  closes  on  its  mouth,  but  escapes  through 
a  valve  in  the  piston  itself  opening  upwards  in  the  same  manner  as  in 
the  barrels  of  the  air  pump.  The  piston  being  raised  again,  the  col- 
umn of  water  ascends  still  higher,  until  it  makes  its  way  through  the 
valve  into  the  exhausting  pipe.  Then  as  the  piston  descends,  the 
water  opens  its  valve,  and  gets  above  the  piston,  and  is  lifted  to  the 
level  of  the  spout,  where  it  is  discharged. 

The  principle  of  the  suction  pump  may  therefore  be  thus  enuncia- 
ted : 

The  water  is  raised  into  the  exhausting  pipe  by  the  pressure  of  the 
atmosphere^  and  thence  lifted  to  the  level  of  the  spout  by  means  of  the 
piston. 

Since  a  column  of  water  thirty  four  feet  in  height,  in  the  suction 
tube,  would  counterbalance  the  entire  pressure  of  the  atmosphere  on 
the  surface  of  the  well,  no  force  would  remain  to  urge  the  column 


168 


PNEUMATICS. 


any  higher,  and  therefore  the  valve   at  the  top  of  the  suction  tube, 
must  be  less  than  thirty  four  feet  above  the  well. 

327.  It  is  evident  that  the  same  force  is  expended  in  raising  water 
by  means  of  the  pressure  of  the  atmosphere,  as  when  the  force  is 
applied  directly.  We  lift  upon  the  atmosphere,  instead  of  lifting  di- 
rectly upon  the  column  of  water.  This  method  of  raising  water 
from  a  well,  is  frequently  more  convenient  than  by  a  simple  bucket, 
but  the  expenditure  of  force  is  the  same  in  both  cases. 

The  Forcing  Pump. 

.  328.  A  cylinder  ABC  (Fig.  75.)  is  placed 
with  its  lower  end  C  in  the  reservoir.  It  has 
a  fixed  valve  at  V,  opening  upwards,  and  a  solid 
piston  without  a  valve,  playing  air  tight  in  the 
upper  barrel  AB.  It  is  connected  with  another 
barrel  DE  by  a  valve  V  opening  upwards  and 
outwards.  The  tube  DE  is  carried  to  whatever 
height  it  may  be  necessary  to  elevate  the  water. 
Let  us  suppose  that  the  solid  piston  P  is  in  con- 
tact with  the  valve  V,  and  that  the  water  in  the 
lower  barrel  is  at  the  same  level  C  with  the  wa- 
ter in  the  reservoir.  Upon  raising  the  piston, 
the  air  in  BC  will  be  rarefied,  and  the  water 
will  ascend  in  BC  exactly  as  in  the  suction-pump. 
Upon  again  depressing  the  piston,  the  air  in  PV 
will  be  depressed,  and  it  will  force  open  the  valve 
V,  and  escape  through  it.  The  process,  there- 
fore, until  water  is  raised  through  V  into  the  upper 
barrel,  is  precisely  the  same  as  for  the  suction  pump,  the  valve  V' 
taking  the  place  of  the  piston-valve  in  that  machine.  Now,  let  us 
suppose  that  water  has  been  elevated  through  V,  and  that  the  space 
PV  is  filled  with  it.  Upon  depressing  the  piston,  this  water,  not  be- 
ing permitted  to  return  through  V,  is  forced  through  V,  and  ascends 
in  the  tube  DE.  By  continuing  the  process,  water  will  accumulate 
in  the  tube  DE,  until  it  acquires  the  necessary  elevation,  and  is  dis- 
charged. Or,  to  enunciate  the  principle  of  this  machine  in  general 
terms — 


STEAM    ENGINE. 


169 


Fig.  76. 


In  the  forcing  pump,  the  piston  has  no  valve,  but  the  water  being 
elevated  into  the  exhausting  tube,  as  in  the  suction  pump,  it  is  then 
forced,  by  the  descent  of  the  piston,  into  the  ascending  pipe  through  a 
valve  placed  in  the  side  and  at  the  bottom  of  the  exhausting  tube. 

329.  In  forcing-pumps,  since  the  power  is  applied  by  separate  im- 
pulses, the  water  would  issue  in  jets,  were  not  some  contrivance  adopt- 
ed to  equalize  its  flow  from  the  tube.     This  purpose  is  effected  by 
means  of  an  air  vessel,  in  which  a  portion  of  condensed  air  is  made 
the  medium  of  communication.     The  force  imparted  by  successive 
blows  of  the  piston  is  first  received  by  this  confined  body  of  air,  and 
this,  by  its  elasticity,  reacts  on  the  surface  of  the  water  in  the  air 
vessel,  and  forces  it  out  by  the  conducting  pipe  or  hose. 

An  example  of  this  is  afforded  in  the  Fire  Engine.  The  fire 
engine  consists  of  two  forcing  pumps,  which  throw  the  water 
into  an  air  vessel,  from  which  it  is  thrown  out  of  the  conducting 
hose  by  the  elastic  pressure  of  condensed  air.  Thus,  (Fig.  76.) 
AB,  AB  are  two  forcing-pumps,  whose 
pistons  P  P  are  wrought  by  a  beam 
whose  fulcrum  is  at  F;  VV  are 
valves  which  open  upwards  from  a 
suction-tube  T,  which  communicates 
with  a  reservoir ;  tt  are  force-pipes, 
which  communicate  by  valves  V'  V, 
opening  into  an  air  vessel  M.  A  tube 
L  is  inserted  in  the  top  of  this  vessel, 
terminating  in  a  leathern  tube  or  hose, 
through  which  the  water  is  forced  by 
the  pressure  of  the  air  confined  in 
M,  which,  in  consequence  of  its  elas- 
ticity, acts  nearly  uniformly  on  the 
surface  of  the  water,  and  forces  it  through  the  hose  in  a  continual 
stream. 

The  Steam  Engine. 

330.  It  belongs  to  Chemistry  to  investigate  the  properties  of  steam 
and  to  Natural  Philosophy  to  apply  it  as  a  mechanical  agent.     The 
Steam  Engine  is  the  fruit  of  the  highest  efforts  of  both  these  sciences, 
and  the  most  valuable  present  ever  made  by  philosophy  to  the  arts. 

22 


170  PNEUMATICS. 

As  it  is  impossible  clearly  to  understand  the  principles  and  construc- 
tion of  this  engine,  without  a  knowledge  of  the  properties  of  steam, 
on  which  they  depend,  we  subjoin  an  account  of  a  few  of  its  lead- 
ing properties,  referring  to  chemical  authors  for  a  more  detailed  view 
of  this  subject. 

331.  The  great  and  peculiar  property  of  steam,  on  which  its  me- 
chanical agencies  depend,  is  its  power  of  creating  at  one  moment  a  high 
degree  of  elastic  force,  and  losing  it  instantaneously  the  next  moment. 
This  force,  acting  on  the  bottom  of  the  piston  which  moves  in  the  main 
cylinder,  raises  it,  and  fills  the   space  below  it  with  steam.     The 
steam  is  suddenly  condensed,   and  hence  no  obstacle  is  opposed  to 
the  descent  of  the  piston,  but  it  is  readily  forced  down  again  by  steam 
acting  from  above.     This  alternate  motion  of  the  piston,  the  rod  of 
which  is  connected  with  the  working  beam,  is  all  that  is  required  in 
order  to  communicate  motion  to  all  parts  of  the  engine. 

332.  The  elastic  force  of  steam  depends  on  its  temperature  and  den- 
sity conjointly;  and  the  temperature  necessary  to  its  production  de- 
pends upon  the  pressure  incumbent  upon  the  water  during  its  forma- 
tion.    The  reason  why  water  boils  at  the  temperature  of  212°  is,  that 
at  that  temperature,  the  vapor  acquires  just  elasticity  sufficient  to  over- 
come the  atmospheric  pressure.     Hence,  steam  produced  at  the  tem- 
perature of  boiling  water,  has  a  force  equal  to  the  pressure  of  the 
atmosphere.     When  formed  at  a  lower  temperature  its  elasticity  di- 
minishes in  a  geometrical  ratio,  and  increases  in  the  same  ratio  when 
it  is  formed  at  a  higher  temperature.     Water  boils,  or  is  converted 
into  vapor,  at  a  temperature  less  than  212°,  on  high  mountains,  or 
under  the  receiver  of  an  air  pump,  or  in  other  situations  where  the 
pressure  of  the  atmosphere  is  diminished  ;  and  in  a  vacuum  the  boil- 
ing point  of  water  is  as  low  as  72°. 

333.  Heat  rapidly  augments  the  elasticity  of  steam  by  increasing  its 
density.     If  we  introduce  a  few  grains  of  water  into  a  flask,  and 
place  it  over  the  fire,  the  water  will  soon  be  converted  into  steam, 
which  will  expel  the  air  of  the  vessel  and  fill  its  whole  capacity.     If 
we  now  close  the  orifice  of  the  flask  and  continue  the  heat,  the  steam 
will  increase  in  elastic  force  in  the  same  manner  as  air  would  do  un- 
der similar  circumstances,  which  is  at  a  comparatively  moderate  rate. 


STEAM    ENGINE.  171 

so  that  it  might  be  heated  'red  hot  without  exerting  any  very  violent 
force.  If,  however,  the  vessel  is  partly  filled  with  water,  and  the 
heat  is  continued  as  before,  then  the  elastic  force  is  rapidly  augment- 
ed, and  becomes  at  length  so  great  as  to  burst  almost  any  vessel  that 
can  be  provided ;  for  every  new  portion  of  vapor  that  is  raised  from 
the  surface  of  the  water,  adds  to  the  density  of  that  which  was  be- 
fore in  the  vessel,  and  proportionally  increases  its  elasticity.  In  the 
experiments  of  Mr.  Perkins,  a  confined  portion  of  steam  not  in  con- 
tact with  water  was  heated  to  the  temperature  of  1400°,  and  still  its 
pressure  did  not  exceed  that  of  five  atmospheres ;  but,  by  injecting 
more  water,  althoagh  the  temperature  was  lessened,  the  elastic  force 

was  gradually  increased  to  one  hundred  atmospheres. 

i 

334.  The  space  into  ivhich  a  given  quantity  of  water  is  expanded 
in  becoming  steam,  depends  upon  the  temperature,  and  of  course 
upon  the  degree  of  pressure,   at  which  it  is  formed.     Water  conver- 
ted into  steam  at  the  temperature  of  212°,  expands  nearly  one  thou- 
sand and  seven  hundred  times;  but  at  the  temperature  of  419°,  it 
expands  but  thirty  seven  times.     According  to  Dr.  Thomson,  at  a 
temperature  not  much  higher  than  500°,  steam  would  not  much  ex- 
ceed double  the  bulk  of  the  water  from  which  it  is  generated.     The 
expansive  force  of  such  steam  would  be  truly  formidable.     It  would, 
when  it  issued  into  the  atmosphere,  suddenly  expand  six  hundred  and 
fifty  times.     We  do  not  know  at  what  temperature  water  would  be- 
come vapor  without  any  increase  of  volume,  but  we  can  estimate  that 
it  would  then  support  a  column  of  mercury  three  thousand  two  hun- 
dred and  forty  three  feet  (or  more  than  half  a  mile)  high,  and  would 
exert  a  pressure  of  nearly  twenty  thousand  pounds  on  every  square 
inch. 

335.  The  difficulty  of  understanding  the  construction  and  princi- 
ples of  the  steam  engine,   (as  is  the  case  also  with  many  other  ma- 
chines where  the  parts  are  numerous,)  is  greatly  enhanced,  by  the 
variety  of  accidental  trappings  or  appendages  that  are  employed  about 
the  machine,  to  perform  subordinate  offices.     As  these  render  the 
comprehension  of  the  leading  principles  difficult,  when  the  explana- 
tion is  attempted  from  the  engine  itself,  so  these  inferior  parts  are 
often  so  multiplied  in  diagrams  as  greatly  to  obscure  the  representa- 


PNEUMATICS. 


lion.  We  shall  begin  our  explanation  with  a  diagram  which  pre- 
sents the  naked  principles  divested  of  all  unnecessary  appendages. 
The  chief  parts  of  the  engine  are  the  boiler  A,  the  cylinder  C,  the 
condenser  L,  and  the  air-pump  M.  B  is  the  steam-pipe,  branching 
into  two  arms  communicating  respectively  with  the  top  and  bottom  of 
the  cylinder ;  and  K  is  the  eduction-pipe,  formed  of  the  two  branches 
which  proceed  from  the  top  and  bottom  of  the  cylinder,  and  commu- 
nicate between  the  cylinder  and  the  condenser.  N  is  a  cistern  or 
well  of  cold  water  in  which  the  condenser  is  immersed.  Each 
branch  of  pipe  has  its  own  valve,  as  F,  G,  P,  Q,  which  may  be  open- 
ed or  closed  as  the  occasion  requires. 


336.  Suppose,  first,  that  all  the  valves  are  open,  while  steam  is  issu- 
ing freely  from  the  boiler.  It  is  easy  to  see  that  the  steam  would  cir- 
culate freely  through  all  parts  of  the  machine,  expelling  the  air,  which 
would  escape  through  the  valve  in  the  piston  of  the  air-pump,  and 
thus  the  interior  spaces  would  be  all  filled  with  steam.  This  process 
is  called  blowing  through :  it  is  heard  when  a  steam-boat  is  about  set- 
ting off.  Next  the  valves  F  and  Q  are  closed,  G  and  P  remaining 
open.  The  steam  now  pressing  on  the  cylinder  forces  it  down,  and 
the  instant  when  it  begins  to  descend,  the  stop  cock  O  is  opened,  ad- 
mitting cold  waier  which  meets  the  steam  as  it  rushes  from  the  cyl- 
inder and  effectually  condenses  it,  leaving  no  force  below  the  piston 


*  From  Jones's  Conversations  on  Chemistry,  a  work  which  contains 
a  very  luminous  view  of  the  elementary  principles  of  the  steam  engine. 


STEAM    ENGINE.  173 

to  oppose  its  descent.  Lastly  G  and  P  being  closed,  F  and  Q  are 
opened,  the  steam  flows  in  below  the  piston  and  rushes  from  above 
it  into  the  cpndenser,  by  which  means  the  piston  is  forced  up  again 
with  the  same  power  as  that  with  which  it  descended.  Meanwhile 
the  air-pump  is  playing,  and  removing  the  water  and  air  from  the 
condenser,  and  pouring  the  water  into  a  reservoir,  whence  it  is  con- 
veyed to  the  boiler  to  renew  the  same  circuit. 

337.  Among  the  different  forces  which  may  be  employed  to  move 
machinery,  such  as  animal  strength,  water,  wind,  and  steam,  the  last 
is  the  most  manageable  of  all,  and  therefore,  for  almost  every  pur- 
pose, the  most  convenient  of  all  powers  that  are  under  the  control  of 
man.     But  whether,  in  a  given  case,  we  shall  employ  steam  power, 
or  one  of  the  other  forces,  as  water  power  for  example,  may  depend 
on  the  comparative  economy  of  the  two  forces.     A  water  fall,  near 
at  hand,  may  furnish  us  with  the  required  power,  cheaper  than  we 
can  produce  it  artificially  from  steam.     In  the  earlier  forms  of  con- 
struction adopted  in  the  Steam  Engine,  so  much  of  the  steam  was 
wasted  by  injudicious  management,  as  greatly  to  diminish  the  useful- 
ness of  this  Engine,  and  to  render  it  in  most  cases  a  less  eligible 
force  for  carrying  machinery  than  animal  strength  or  water.     The 
modern  improvements  in  the  Steam  Engine  have  consisted,  mainly, 
in  preventing  this  waste  of  steam,  and  of  course  in  economizing  the 
amount  of  fuel  required  to  produce  the  power.     Previous  to  the 
year  1763,  when  Watt  began  his  improvements  on  the  steam  engine, 
not  less  than  three  fourths  of  the  steam  produced  in  the  boiler  was 
wasted. 

338.  The  greatest  improvement  introduced  by  Mr.  Watt,  consist- 
ed in  performing  the  condensation  in  a  separate  vessel,  (L,  Fig.  77.) 
whereas  the  previous  method  was  to  admit  a  jet  of  cold  water  into 
the  cylinder  (CC)  itself,  which  cooled  the  whole  apparatus;  and 
when  steam  was  admitted  again  from  the  boiler,  a  great  quantity  of 
it  was  consumed  in  heating  the  cooled  surface  up  to  the  boiling  point, 
which  must  be  done  before  the  steam  could  have  sufficient  elasticity 
to  move  the  machinery.     Various  subordinate  contrivances  were  also 
employed,  with  the  view  of  promoting  convenience  or  economy,  the 
principal  of  which  will  be  understood  from  the  description  of  the 


174  PNEUMATICS. 

annexed  plate,  which  represents  the  steam  engine  in  its  most  im- 
proved state. 

339.  A.  The  BOILER,  containing  a  large  quantity  of  water  which 
is  constantly  renewed  as  fast  as  portions  are  converted 
into  steam* 

B.  The  STEAM  PIPE,  conveying  the  steam  to  the  cylinder, 

having  a  steam-cock  b  to  admit  or  exclude  the  steam 
at  pleasure. 

C.  The  CYLINDER,  surrounded  by  the  jacket  c  c,  a  space 

kept  constantly  supplied  with  hot  steam,  in  order  to 
keep  the  cylinder  from  being  cooled  by  the  external 
air. 

D.  The  EDUCTION  PIPE,  communicating  between  the  cyl- 

inder and  the  condenser. 

E.  The  CONDENSER,  with  a  valve  e,  called  the  Injection 

cock,  admitting  a  jet  of  cold  water,  which  meets  the 
steam  the  instant  the  latter  enters  the  condenser. 

F.  The  AIR  PUMP,  which  is  a  common  suction  pump,  but 

is  called  the  air  pump  because  it  removes  from  the 
condenser  not  only  the  water,  but  also  the  air  and 
steam  that  escapes  condensation. 

G.  G.  The  COLD  WATER  CISTERN,  which  surrounds  the  con- 
denser and  supplies  it  with  cold  water,  being  filled  by 
H.  The  COLD  WATER  PUMP. 

I.  The  HOT  WELL,  containing  water  from  the  condenser. 

K.  The  HOT  WATER  PUMP,  which  conveys  back  the  water 

of  condensation  from  the  hot  well  to  the  boiler. 

L.  L.  LEVERS,  which  open  and  shut  the  valves  in  the  channel 
between  the  steam  pipe,  cylinder,  eduction  pipe,  and 
condenser ;  which  levers  are  raised  or  depressed  by 
projections  attached  to  the  piston  rod  of  the  con- 
denser. 

M.  M.  Apparatus  for  PARALLEL  MOTION.  By  this  contrivance 
the  pis-ton  rod  is  made  to  move  in  a  right  line,  although 
the  end  of  the  working  beam  moves  in  the  arc  of  a 
circle. 

N.  N.  The  WORKING  BEAM. 


STEAM    ENGINE.  175 

O.  O.  The  GOVERNOR.  This  consists  of  two  heavy  balls, 
suspended  from  a  perpendicular  shaft  in.  such  a  man- 
ner as  to  be  capable  of  falling  close  to  the  side  of  the 
shaft  when  at  rest,  but  when  made  to  revolve,  they 
recede  from  it  by  the  centrifugal  force.  Now,  by 
connecting  the  governor  with  the  fly  wheel,  it  is  made 
to  participate  of  the  common  motion  of  the  engine, 
and  the  balls  will  remain  at  a  constant  distance  from 
the  perpendicular  shaft,  so  long  as  the  motion  of  the 
engine  is  uniform ;  but  whenever  the  engine  moves 
faster  than  usual,  the  balls  will  recede  farther  from 
the  shaft,  and  by  raising  a  valve  connected  with  the 
boiler,  will  let  off  such  a  portion  of  the  force  as  to 
reduce  the  speed  to  the  rate  required. 
P.  The  CRANK.  This,  when  the  end  of  the  working  beam, 
to  which  it  is  attached,  descends,  turns  the  fly  wheel 
half  round,  and  when  it  rises,  completes  the  revolu- 
tion of  the  wheel. 

Q.  Q.  The  FLY  WHEEL.  The  motion  of  the  piston,  being 
communicated  first  to  the  Working  Beam,  and  thence 
to  the  crank,  is  finally  received  by  the  Fly  Wheel, 
which,  by  its  inertia,  as  explained  in  Art.  193.  ren- 
ders the  force  uniform.  The  main  shaft  or  axis  to 
which  the  fly  wheel  is  attached,  receiving 'thus  a  uni- 
form rotation,  motion  may  be  transferred  from  it  to 
every  part  of  the  machinery. 

340.  The  kind  of  valve  chiefly  employed  in  the  steam  engine  is 
that  called  the  puppet  valve*  It  resembles  the  stopper  of  a  decan- 
ter, but  is  more  obtuse.  All  these  various  appendages  of  the  ma- 
chine, are  carried  by  the  engine  itself;  the  air  pump  is  worked  by 
having  its  piston  rod  attached  to  one  arm  of  the  working  beam,  and 
the  valves  are  opened  at  the  instant  required  by  means  of  levers,  to 
which  also  motion  is  communicated  from  the  same  source. 


*  Several  examples  are  seen  in  the  plate,  on  the  right  of  the  cylin- 
der, above  arid  below. 


176 


PNEUMATICS. 


341.  Soon  after  the  invention  of  these  engines,  Watt  found  that,  in 
some  instances,  inconvenience  arose  from  the  too  rapid  motion  of  the 
steam  piston  at  the  end  of  its  stroke,  owing  to  its  being  meved  with 
an  accelerated  motion.*     This  was  owing  to  the  uniform  action  of  the 
steam  pressure  upon  it.     For  on  first  putting  it  in  motion,  at  the  top 
of  the  cylinder,  the  motion  was  comparatively  slow1,  but  from  the  con- 
tinuance of  the  same  pressure,  the  velocity  with  which  the  piston  de- 
scended was  continually  increasing,  until  it  reached  the  bottom  of  the 
cylinder,  when  it  acquired  its  greatest  velocity.     To  prevent  this, 
and  to  render  the  descent  as  nearly  uniform  as  possible,  it  was  pro- 
posed to  cut  off  the  steam  before  the  descent  was  completed,  so  that 
the  remainder  might  be  effected  merely  by  the  expansion  of  the 
steam  which  was  admitted  to  the  cylinder,  f     To  accomplish  this  he 
contrived,  by  means  of  a  pin  on  the  rod  of  the  air-pump,  to  close  the 
upper  steam-valve  when  the  steam-piston  had  completed  one  third 
of  its  entire  descent,  and  to  keep  it  closed  during  the  remainder  of 
that  descent,  and  until  the  piston  again  reached  the  top  of  the  cylin- 
der.    By  this  arrangement,  the  steam  pressed  the  piston  with  its  full 
force  through  one  third  of  the  descent,  and  thus  put  it  in  motion ; 
during  the  other  two  thirds  of  the  way,  the  steam  thus  admitted  acted 
merely  by  its  expansive  force,  which  became  less  in  exactly  the  same 
proportion  as  the  space,  given  to  it  by  the  descent  of  the  piston,  in- 
creased.    Thus,  during  the  last  two  thirds  of  the  descent,  the  piston 
is  urged  by  a  gradually  decreasing  force,  which  in  practice  is  found 
just  sufficient  to  keep  up  in  the  piston  a  uniform  velocity.     Another 
advantage  gained  by  this  contrivance  independently  of  the  uniformity 
of  motion  was,  that  two  thirds  of  the  fuel  was  saved ;  for  instead  of 
consuming  a  cylinder  full  of  steam  each  descent  of  the  piston,  only 
one  third  of  a  cylinder  was  necessary. 

342.  As  an  example  of  a  self-regulating  machine,  the  Steam  En- 
gine surpasses  all  other  forms  of  machinery.     On  this  subject  Dr. 


*  For  since  the  steam  continues  to  act  upon  the  piston  during  its 
descentv-its  velocity  would  be  constantly  increased,  like  that  of  a  ball 
in  the  barrel  of  a  gun. 

t  Steam  engines  constructed  on  this  principle  are  said  to  act  ex- 
pansively. 


VV'.\TT\S 


ACOUSTICS. 


177 


Arnott  has  the  following  remarks.  "  The  Steam  Engine,  (says  he,) 
in  its  present  improved  state,  appears  to  be  a  thing  almost  endowed 
with  intelligence.  It  regulates,  with  perfect  accuracy  and  uniformity* 
the  number  of  its  strokes  in  a  given  time,  and,  moreover,  counts  or 
records  them,  to  tell  how  much  work  it  has  done,  as  a  clock  records 
the  beats  of  its  pendulum.  It  regulates  the  supply  of  water  to  the 
boiler,  the  briskness  of  the  fire,  and  the  quantity  of  steam  admitted 
to  work ;  opens  and  shuts  its  valves  with  absolute  precision ;  oils  its 
joints  5  takes  out  any  air  which  may  accidentally  enter  into  parts 
where  a  perfect  vacuum  is  required ;  and  when  any  thing  goes  wrong 
which  it  cannot  of  itself  rectify,  it  warns  its  attendants-  by  ringing  a 
bell.  Yet  with  all  these  talents  and  qualities,  and  even  when  pos- 
sessing the  power  of  600  horses,  it  is  obedient  to  the  hand  of  a  child. 
Its  aliment  is  coal,  wood,  charcoal,  or  other  combustible ;  but  it  con- 
sumes none  while  idle.  It  never  tires,  and  wants  no  sleep ;  it  is  not 
subject  to  any  malady  when  originally  well  made,  and  only  refuses 
to  work  when  worn  out  with  age.  It  is  equally  active  in  all  climates, 
and  will  do  work  of  any  kind.  It  is  a  water  pumper,  a  miner,  a 
sailor,  a  cotton  spinner,  a  weaver,  a  blacksmith,  a  miller  >  and  a  small 
engine  in  the  character  of  a  steam  poney,  may  be  seen  dragging 
after  it  on  a  rail  road  a  hundred  tons  of  merchandize,  or  a  regiment 
of  soldiers,  with  greater  speed  than  that  of  our  fleetest  coaches.  It 
is  the  king  of  machines,  and  a  permanent  relization  of  the  Genii  of 
eastern  fable,  whose  supernatural  powers  were  occasionally  at  the 
command  of  man." 


CHAPTER  V. 

OF  ACOUSTICS, 

343.  ACOUSTICS  w  the  science  which  treats  of  the  nature  and 
laws  of  SOUND. 

« 

In  comparing  substances  which  have  different  properties  in  respect 
to  sound^  as  lead  and  glass,  we  shall  find  them  distinguished  from 
each  other  by  the  degree  of  vibration  which  they  are  capable  of  re- 
ceiving, and  by  the  length  of  time  during  which  they  can  preserve 
a  vibratory  motion ;  those  substances  which  are  most  capable  of  vi- 

23 


1*78  PNEUMATICS. 

bration  being  most  sonorous,  and  those  which  can  longest  maintain  a 
stale  of  vibration,  also  persevering  longest  in  emitting  sound.  Bodies, 
though  of  the  same  substance,  differ  in  these  respects  according  as 
their  form  varies ;  those  forms  which  are  most  favorable  to  the  pro- 
duction and  continuance  of  a  vibratory  motion,  being  also  most  favor- 
able to  the  production  and  permanence  of  sound.  Thus,  a  hollow 
globe  of  brass  is  far  less  sonorous  than  the  hemispheres  which  are 
made  by  dividing  it  into  two  equal  parts,  since  the  structure  of  a 
globe  is  such  that  the  parts  mutually  support  each  other,  like  a  con- 
tinued arch,  while  the  form  of  the  hemispheres,  which  approaches 
that  of  a  bell,  is  peculiarly  liable  to  a  tremulous  vibratory  motion. 
Indeed,  when  a  body  sounds  powerfully,  as  a  large  bell,  or  the  lowest 
string  of  a  harpsichord,  we  can  -perceive  that  it  actually  vibrates ; 
and  even  in  cases  where  the  vibration  is  imperceptible  to  the  naked 
eye,  we  may  detect  it  by  the  microscope,  or  by  some  other  artifice. 
Thus,  if  we  put  some  water  into  a  glass  tumbler  or  basin  and  make 
it  sound,  by  applying  the  moistened  finger,  the  water  will  be  agitated. 
If  we  hold  the  hand  over  the  pipe  of  an  organ,  we  shall  feel  a  trem- 
ulous motion  in  the  air  passing  through  it.  Such  experiments  may 
be  extended  to  all  solid  bodies  by  placing  upon  them  pieces  of  paper 
or  strewing  them  with  fine  sand.  Hence, 

Vibrations,  in  the  sounding  body,  are  the  immediate  cause  of  sound. 

344.  The  pitch  of  musical  strings,  is  found  by  experience  to  de- 
pend on  three  circumstances  5  the  length  of  the  string, — its  weight, 
or  quantity  of  matter, — and  its  tension.     The  tone  becomes  more 
acute  as  we  increase  the  tension,  or  diminish  either  the  length  or  the 
weight.     The  operation  of  these  several  circumstances  may  be  seen 
in  a  common  violin.     The  pitch  of  any  one  of  the  strings  is  raised 
or  lowered  by  turning  the  screw  so  as  to  increase  or  lessen  its  tension ; 
or,  the  tension  remaining  the  same,  higher  or  lower  notes  are  pro- 
duced by  the  same  string,  by  applying  the  fingers  in  such  a  manner 
as  to  shorten  or  lengthen  the  string  which  is  vibrating ;  or,  both  the 
tension   and  the  Jength  of  the  strhig  remaining  the  same,  the  pitch 
is  altered  by  making  the  string  larger  or  smaller  and  thus  increasing 
w  diminishing  its  weight. 

345.  The  vibrations  of  a  string,  fixed  at  both  ends,  are  performed 
in  equal  times,  whether  the  length  of  the  vibrations  be  greater,  or 
smaller. 


ACOUSTICS.  179 

Upon  this  uniformity  in  the  times  of  vibration  depends  the  uni- 
formity of  tone ;  for  if  we  employ  a  string  of  unequal  thickness, 
and  consequently  one  whose  vibrations  are  performed  in  different 
times,  the  sound  is  confused  and  variable,  and  any  other  mode  by 
which  we  destroy  the  isochronism,  produces  a  similar  effect.  The 
same  law  has  been  found  to  extend  to  all  other  cases  of  musical 
sounds ;  and,  therefore,  we  may  conclude,  that  isochronism  in  the 
vibrations  of  sonorous  bodies,  is  essential  to  their  producing  musical 
sounds. 

346.  In  wind  instruments,  a  column  of  confined  air  itself  is  the 
vibrating  body ;  and  here  the  vibrations  are  longitudinal  instead  oi 
lateral,  as  is  the  case  with  strings.     That  it  is  really  the  air  whicli 
is  the  sounding  body  in   a  flute,  organ  pipe,  or  other  wind  instru- 
ment,  appears  from  the  fact,  that  the  materials,  thickness,  or  other 
peculiarities  of  the  pipe,  are  of  no  consequence.     A  pipe  of  paper 
and  one  of  lead,  glass,  or  wood,  provided  the  dimensions  are  the 
same,  produce,  under  similar  circumstances,  exactly  the  same  tone 
as  to  pitch.     If  the  qualities  of  the  tones  produced  by  different  pipes 
differ,  this  is  to  be   attributed  to  the  friction  of  the  air  within  them, 
setting,  in  feeble  vibration,  their  own  proper  materials.     The  class 
of  bodies  vibrating  longitudinally,  is  not  only  more  diversified  in  its 
powers  than  the  other  classes  of  sounding  bodies,  but  also  more  ex- 
tensive in  the  range  of  substances  which  it  comprehends. 

347.  The  different  pitch  of  bodies  vibrating  longitudinally,  and 
free  at  both  extremities,  depends  on  four  circumstances,  viz.  their 
elasticity,  the  temporary  rate  at  which  their  elasticity  is  increased  by 
condensation,  their  length,  and  their  specific  gravity,  the  tone  of  a 
body  being  more  acute,   according  as  the  elasticity,  and  the  rate  of 
its  increase  by  condensation,  are  greater,  or  the  length  and  specific 
gravity  less.     The  length  of  the  sonorous  body  is  almost  exclusively 
the  only  one  of  these  circumstances  which  we  have  completely  in 
our  power ;  and  with  regard  to  ordinary  wind  instruments,   and  all 
musical  instruments  where  common  air  is  the  vibrating  body,  the 
length  is  the  circumstance  of  most  importance,  since  the  elasticity, 
rate  of  condensation,  and  specific  gravity  are  then  nearly  constant 
quantities.     The  change  of  specific  gravity,  however,  to  which  the 


180  PNEUMATICS. 

air  is  subject  in  consequence  of  changes  of  temperature,  materially 
affects  the  pitch  of  wind  instruments.  The  frequency  of  vibration 
of  a  column  of  air  is  found  to  be  increased  about  g\,  by  an  elevation 
of  30°  Fahrenheit.  Thus,  the  tone  of  an  organ  has  been  found  to 
be  higher  in  summer  than  in  winter ;  and  flutes  and  other  wind  in- 
struments become  gradually  more  acute  as  the  included  air  is  heated 
by  the  breath. 

348.  If  a  bett  be  struck  by  a  clapper  on  the  inside,  the  bell  is 
made  to  vibrate.     The  base  of  the  bell  is  a  circle ;  but  it  has  been 
found  that,  by  striking  any  part  of  the  circle  on  the  inside,  that  part 
flies  out,  so  that  the  diameter  which  passes  through  this  part  of  the 
base,  will  be  longer  than  the  other  diameters.     The  base  is  chang- 
ed by  the  blow  into  the  figure  of  an  ellipse,  whose  longer  axis  pass- 
es through  the  part  against  which  the  clapper  is  thrown.     The  elas- 
ticity of  the  bell  restores  the  figure  of  the  base,  and  again  elongates 
the  bell  in  a  direction  opposite  to  the  former ;  and  the  two  elliptical 
figures  thus  alternate  with  each  other,  growing  smalller  and  smaller, 
like  the  vibrations  of  a  pendulum  when  ihe  moving  force  is  with- 
drawn, until  the  sound  dies  away.     We  may  be  convinced  by  our 
senses,  that  the  parts  of  the  bell  are  in  a  vibratory  motion  while  it 
sounds.     If  we  lay  the  hand  gently  upon  it,  we  shall  feel  this  tremu- 
lous motion,  and  even  be  able  to  stop  it ;  or  if  small  pieces  of  paper 
be  put  upon  the  bell,  its  vibrations  will  set  them  in  motion. 

We  may  conceive  the  bell  to  be  formed  of  an  infinitude  of  rings, 
placed  one  above  another  from  the  base  to  the  highest  point.  The 
rings  situated  nearer  to  the  base,  having  a  greater  circumference, 
tend  to  perform  their  vibrations  more  slowly,  while  the  rings  nearer 
to  the  summit,  whose  circumferences  are  smaller,  tend  to  produce 
vibrations  oftener.  These  sounds  will  so  coalesce  as  to  produce  a 
mixed  sound,  intermediate  between  those  of  the  higher  and  lower 
rings, 

Propagation  of  Sound. 

349.  AIR  is,  in  general,  the  medium  of  sound.     A  bell  struck 
under  the  receiver  of  an  air  pump,  gives  a  feebler  and  feebler  sound 
as  the  exhaustion  proceeds,  until,  when  the  rarefaction  is  carried  to 
9  certain  extent,  it  emits  no  sound  at  all.     Hence,  on  the  summit  of 


ACOUSTICS.  181 

high  mountains,  where  the  air  is  naturally  rare,  sound  ought  to  be 
weaker  than  at  the  general  level  of  the  earth ;  and  such  is  found  to 
be  the  fact.  Saussure  relates  that  upon  the  top  of  Mount  Blanc,  the 
firing  of  a  pistol  made  a  report  no  louder  than  that  of  a  child's  toy- 
gun.  A  fact  mentioned  by  travellers  in  Alpine  countries,  is  explained 
on  this  principle.  They  see  distinctly  a  huntsman  on  a  neighboring 
eminence,  and  observe  the  flashes  of  his  gun,  but  can  scarcely  hear 
the  report,  even  when  comparatively  near  them. 

350.  The  agency  of  air  as  the  medium  of  sounds  may  be  briefly 
expressed  thus : 

Air  receives  from  sounding  bodies  vibrations,  which  it  communi- 
cates to  the  organs  of  hearing. 

In  an  open  space,  and  in  a  serene  atmosphere,  sound  is  propoga- 
ted  from  the  sounding  body  in  all  directions.  Sounds,  even  the  most 
powerful,  when  thus  transmitted  freely  through  the  air,  diminish  ra- 
pidly in  force,  as  they  depart  from  their  sources,  and  within  moderate 
distances  wholly  die  away.  What  law  this  dimunition  follows,  is  not 
yet  ascertained  ;  and  is,  indeed,  in  the  present  state  of  Acoustics, 
incapable  of  determination.  Some  writers  have  supposed  that  sound 
follows  the  common  law  of  emanations  radiating  from  a  center,  and, 
consequently,  that  its  intensity  at  different  distances  from  its  source 
varies  inversely  as  the  square  of  the  distance ;  but  we  can  estimate 
the  force  of  sounds  by  the  ear  alone ;  an  instrument  of  comparison 
whose  decisions  on  this  point  vary  with  the  bodily  state  of  the  observ- 
er, and  whose  scale  expresses  no  definite  relation  but  that  of  equal- 
ity. Though  sound  has  in  general,  at  its  origin,  a  tendency  to  dif- 
fuse itself  in  all  directions,  it  is  sometimes  more  propogated  in  one 
direction  than  in  others.  A  cannon  seems  much  louder  to  those  who 
stand  immediately  before  it,  than  to  those  who  are  placed  behind  it. 
The  same  fact  is  illustrated  by  the  speaking  trumpet ;  the  person  to- 
wards whom  the  instrument  is  directed,  hears  distinctly  the  words 
spoken  through  it,  while  those  who  are  situated  a  little  to  one  side, 
hardly  perceive  any  sound. 

351.  Sound  is  in  a  great  measure  intercepted  by  the  intervention 
of  any  solid  obstacle  between  the  hearer  and  the  sonorous  body, 


182  PNEUMATICS. 

Thus,  if  while  a  bell  is  sounding,  houses  intervene  between  us  and 
the  bell,  we  hear  it  sound  but  faintly  compared  with  what  we  hear 
after  we  have  turned  the  corner  of  the  building.  From  this  fact 
sound  would  seem  to  be  propagated  in  straight  lines.  If,  however, 
we  «peak  through  a  tube,  the  voice  will  be  wholly  confined  by  the 
tube,  and  will  follow  its  windings  however  tortuous ;  hence  we  infer 
that  sound  is  propagated  not  in  right  lines  like  radiant  substances  as 
heat  and  light,  but  in  undulations,  after  the  manner  of  waves,  such 
as  follow  when  a  stone  is  thrown  into  still  water. 

352.  Though  air  is  the  most  common  medium  of  sound,  yet  it  is 
not  the  only  medium.     Various  other  bodies  both  solid  and  fluid, 
are  excellent  conductors  of  sound ;  and  the  fainter  sound  of  the  bell 
when  buildings  intervene,  as  in   the  case  supposed,  arises  from  the 
fact  that  sound  passes  with  difficulty  from  one  medium  into  another. 
If  a  log  of  wood  is  scratched  with  a  pin  at  one  extremity,  a  person 
who  applies  his  ear  to  the  other  extremity  will  hear  the  sound  dis- 
tinctly,  and  when  a  long  pole  of  wood  is  applied  at  one  end  to  the 
teeth,  the  ticking  of  a  watch  may  be  heard  at  the  other  end,  at  a 
much  greater  distance,  than  when  there  is  no  medium  of  communica- 
tion but  the  air.     The  motion  of  a  troop  of  cavalry  is  heard  at  a 
great  distance  by  applying  the  ear  close  to  the  ground,  and  it  is  well 
known  that  dogs  by  this  method  first  discover  the  approach  of  a 
stranger.  v 

353.  The  VELOCITY  of  sound  is  progressive.     Thus  when  a  gun 
is  fired  at  a  distance  from  us,  we  perceive  the  flash  some  time  before 
we  hear  the  report.     Thunder  follows  the  lightning  at  a  perceptible 
interval,   although  they  are  known  to  be  cotemporaneous  events.     If 
a  gun  be  fired  at  a  certain  known  distance,  and  we  observe  the  in- 
terval between  the  flash  and  the  report,  we  may  obtain  the  rate  at 
which  sound  passes,  that  is  the  velocity  of  sound.     Many  years  since 
Dr.   Derham  made  a  number  of  accurate  and  diversified  experi- 
ments on  this  subject,  and  fixed  the  velocity  of  sound  at  1142  feet 
per  seepnd.     The  mean  of  a  great  number  of  experiments  give  the 
average  velocity  of  1 130  feet  per  second  ;  but  the  velocity  as  deter- 
mined by  Derham,  namely,  1142  feet  per  second,  is  that  which  has 
been  generally  admitted  as  the  standard.     Since,  however,  the  trans- 


ACOUSTICS,  183 

mission  of  sound  depends  on  the  elasticity  of  the  medium,  (Art.  347.) 
causes  which  affect  the  elasticity,  likewise  affect  the  velocity  of  sound, 
Thus,  the  velocity  is  a  little  greater  in  warm  than  in  cold  air,  and 
consequently  is  somewhat  influenced  by  climate. 

354.  Sound  moves  with  a  uniform  velocity ;  that  is,  it  passes  over 
equal  spaces  in  equal  times.     This  important  fact  was  first  ascertain- 
ed by  Derham,  who  found  that  it  held  good  whether  the  sound  were 
strong  or  feeble,  whether  it  proceeded  from  a  hammer  or  a  cannon : 
iu  short,  that  neither  the  strength  nor  the  origin  of  the  sound  made 
any  difference.     M.  Biot  caused  several  airs  to  be  played  on  a 'flute 
at  the  end  of  an  iron  pipe  3120  feet  long,  and  the  notes  were  dis- 
tinctly heard  by  him  at  the  other  end,  without  the  slightest  derange- 
ment in  the  order  or  quality  of  the  sounds.     The  velocity  of  sound, 
however,  when  transmitted  through  the  air,  is  slightly  influenced  by 
the  strength  and  direction   of  'the  wind.     Dr.   Derham  found  that 
when  the  wind  is  blowing  in  the  direction  of  the  sound,  its  velocity 
must  be  added  to  the  standard  velocity  of  sound,  and  must  be  sub- 
tracted from  it  when  opposed  to  it.     A  transverse  wind  does  not  affect 
the  velocity  of  sound  in  the  slightest  degree. 

355.  From  a  knowledge  of  the  velocity  of  sound,  the  distance  of 
a  sounding  body  may  be  estimated.     Thus  if  the  interval  between 
seeing  a  flash  of  lightning,  and  hearing  the  thunder  be  six  seconds 
the  distance  of  the  cloud  is  6  X  1 142  =  6852  feet,  or  IfV  miles.     The 
air  is  a  better  conductor  of  sound  when  humid  than  when  dry.     Thus 
a  bell  is  heard  better  just  before  a  rain  ;  and  this  fact  lends  some 
countenance  to  an  opinion  of  the  ancients,  that  sound  is  heard  better 
by  night  than  by  day.     Humboldt  was  particularly  struck  with  this 
fact,  when  he  heard  the  noise  of  the  great  cataracts  of  Orinoco,  which 
he  describes  as  three  times  greater  in  the  night  than  in  the  day.     The 
distance  to  which  sound  may  be  heard,  will  of  course  vary  with  its 
force  and  various  other  circumstances  which  are  incapable  of  being 
reduced  to  an  exact  law.     Volcanoes,  in  South  America,  have  some- 
times been  heard  at  the  distance  of  three  hundred  miles ;  and  naval 
engagements  have  been  heard  at  the  distance  of  two  hundred  miles. 
The  unassisted  human  voice  has  been  heard  from  Old  to  New  Gib- 
raltar, a  distance  of  ten  or  twelve  miles,  the  watchword  All's  Well 
given  at  the  former  place  being  heard  at  the  latter.     Sounds  are 


184  PNEUMATICS. 

heard  to  a  much  greater  distance  over  water  than  over  land,  and  far- 
ther on  smooth  than  on  rough  surfaces. 

356.  Liquors  are  good  conductors  of  sound.     Indeed,  sound  is 
conveyed  with  far  greater  velocity  in  water  than  in  air,  and  this  too  in 
consequence  of  its  greater  elasticity;  for,  since  water  has  been  found 
by  Perkins  and  others,  capable  of  compression  and  of  restoring  itself 
when  the  compressing  force  is  removed,  it  is  to  be  accounted  not 
only  elastic,  but  as  exceeding  triform  bodies  in  elasticity  in  proportion 
as  the  force  required  to  compress  it  is  greater.     Dr.  Franklin,  hav- 
ing plunged  his  head  below  water,  caused  a  person  to  strike  two 
stones  together  beneath  the  surface,  and  heard  the  sound  distinctly  at 
the  distance  of  more  than  half  a  mile.     By  similar  experiments,  it 
has  been  ascertained,  that,  though  water  is  a  much  better  conductor 
of  sound  than  air,  yet  the  sound  is  greatly  enfeebled  by  passing  out 
of  one  medium  into  the  other. 

357.  Solid  substances  convey  sound  with  various  degrees  of  facili- 
ty, but  in  general  much  better  than  air,  and  as  well  or  even  better  than 
fluids.     By  placing  the  ear  against  a  long  dry  brick  wall,  and  caus- 
ing a  person  at  a  considerable  distance  to  strike  it  once  with  a  ham- 
mer, the  sound  will  be  heard  twice,  because  the  wall  will  convey  it 
with  greater  rapidity  than  the  air,  though  each  will  bring  it  to  the  ear. 
The  rate  at  which  cast  iron  conducts  sound,  was  ascertained  by  M. 
Biot  in  the  following  manner.     He  availed  himself  of  the  laying  of 
a  series  of  iron  pipes  to  convey  water  to  Paris.     The  pipes  were 
about  eight  feet  in  length,  and  were  connected  together  with  small 
leaden  rings.     A  bell  being  suspended  within  the  cavity,  at  one  end 
of  the  train  of  pipes,  on  striking  the  clapper  at  the   same  instant 
against  the  side  of  the  bell,  and  against  the  inside  of  the  pipe,  two 
distinct  sounds  successively  were  heard  by  an  observer  stationed  at 
the  other  extremity.     With  a  train  of  iron  pipes  two  thousand  five 
hundred  and  fifty  feet,  or  nearly  half  a  mile  in  length,  the  interval  be- 
tween the  two  sounds  was  found  from  a  mean  of  two  hundred  trials, 
to  be  1.79  seconds.     But  the  transmission  of  sound  through  the  in- 
ternar'eolumn  of  air,  'would  have  taken  2.2  seconds ;  which  shows 
that  the  sound  occupied  only  .41  of  a  second  in  passing  through  the 
metal.     From  more  direct  trials,  it  was  concluded  that  the  exact  in- 
terval of  time,  during  which  the  sound  performed  its  passage  through 


ACOUSTICS. 


185 


the  substance  of  the  train  of  pipes,  amounted  to  only  the  .26  of  a 
second,  showing  that  iron  conducts  sound  about  ten  times  as  rapidly 
as  air  does.  If  a  string  be  tied  to  a  common  fire  shovel,  and  the  two 
ends  of  the  string  be  wound  around  the  fore  fingers  of  each  hand, 
and  the  fingers  be  placed  in  the  ears,  on  striking  the  bottom  of  the 
shovel  against  an  andiron  or  other  solid  body,  very  deep  and  heavy 
tones  will  be  heard,  and  the  vibrations  of  the  metal  will  be  clearly 
perceived. 

The  great  power  of  solid  bodies  to  conduct  sound  is  exemplified 
in  earthquakes,  which  are  heard  almost  simultaneously  in  very  dis- 
tant parts  of  the  earth.  Musical  boxes  sound  much  louder  when 
placed  on  a  table  or  some  solid  support,  than  when  the  air  affords  the 
only  conducting  medium.  It  is  easy  to  ascertain  whether  a  kettle 
boils,  by  putting  one  end  of  a  stick  or  poker  on  the  lid,  and  the  other 
end  to  '  the  ear :  the  bubbling  of  the  water,  when  it  boils,  appears 
louder  than  the  rattling  of  a  carriage  in  the  streets.  A  slight  blow 
given  to  the  poker,  of  which  the  end  is  held  to  the  ear,  produces  a 
sound  which  is  even  painfully  loud. 

358.  A  physician  of  Paris  introduced  into  medical  practice  an  in- 
strument, depending  on  the  power  of  solid  bodies  to  conduct  sound, 
called  the  Stethoscope,  the  object  of  which  is  to  render  audible  the 
action  of  the  heart  and  the  neighboring  organs.  It  consists  of  a 
wooden  cylinder,  one  end  of  which  is  applied  firmly  to  the  breast, 
while  the  other  end  is  brought  to  the  ear.  By  this  means,  the  pro- 
cesses that  are  going  on  in  the  organs  of  respiration,  and  in  the  large 
blood  vessels  about  the  heart,  may  be  distinctly  heard  ;  and  it  is  said 
that  the  stethoscope,  when  skillfully  used,  "  becomes  the  means  of 
ascertaining  some  diseases  in  the  chest,  almost  as  effectually  as  if 
there  were  convenient  windows  for  visual  inspection." 

Reflexion  of  Sound. 

3&9.  Sounds  are  reflected  by  hard  bodies,  producing  the  well 
known  phenomenon  called  an  ECHO.  If  a  straight  line  be  drawn 
from  the  sounding  body  to  the  reflecting  surface  representing  the 
course  of  the  sound  before  reflexion,  and  another  straight  line  be 
drawn  from  the  reflecting  surface,  in  the  direction  of  the  sound  after 
reflexion,  these  two  lines  will  make  equal  angles  with  that  surface ; 

24 


186  PNEUMATICS. 

that  is,  when  sound  is  reflected,  the  angle  of  reflexion  is  equal  to  the 
angle  of  incidence.  The  surfaces  of  various  bodies,  solids  as  well  as 
fluids,  have  been  found  capable  of  reflecting  sounds,  viz.  the  sides 
of  hills,  houses,  rocks,  banks  of  earth,  the  large  trunks  of  trees,  the 
surface  of  water,  especially  at  the  bottom  of  a  well  and  sometimes 
even  the  clouds.  It  is  therefore  evident  that  in  an  extensive  plain,  or 
at  sea,  where  there  is  no  elevated  body  capable  of  reflecting  sounds, 
no  echo  can  be  heard.  It  is  hence  easy  to  see  why  the  poets,  who 
convert  Echo  into  an  animated  being,  place  her  habitation  near 
mountains,  rocks,  and  woods.  An  echo  is  heard  when  a  person  stands 
in  a  position  to  hear  both  the  original  and  the  reflected  sound ;  and 
the  interval  will  be  greater  or  less  according  to  the  distance  of  the 
reflecting  surface  from  the  sounding  body  and  from  the  hearer,  and 
hence  the  interval  may  be  made  a  measure  of  the  distance.  If  the 
sound  of  the  voice  returns  to  the  speaker  in  two  seconds,  the  distance 
of  the  reflecting  surface  is  one  thousand  one  hundred  and  forty  two 
feet,  and  in  that  proportion  for  other  intervals.  Thus  the  breadth  of 
a  river  may  be  ascertained  when  there  is  an  echoing  rock  on  the  farther 
shore.  A  perpendicular  mountain's  side,  or  lofty  cliffs,  such  as  fre- 
quently skirt  the  sea  coast,  sometimes  returning  an  echo  of  the  dis- 
charge of  artillery,  or  of  a  clap  of  thunder,  to  the  distance  of  many 
miles.  The  number  of  syllables  that  can  be  pronounced  in  half  the 
interval,  will  be  repeated  distinctly ;  but  a  greater  number  would  be 
blended  with  the  commencement  of  the  echo. 

3GO.  The  furniture  of  a  room,  especially  the  softer  kind,  such 
as  curtains  or  carpets,  impair  the  qualities  of  sound  by  presenting 
surfaces  unfavorable  to  vibrations.  A  crowded  audience  has  a  simi- 
lar effect,  and  increases  the  difficulty  of  speaking.  Halls  for  music 
or  declamation,  should  be  constructed  with  plain  bare  walls.  Alcoves, 
recesses,  and  vaulted  ceilings,  produce  reverberations  which  often 
greatly  impair  the  distinctness  of  elocution.  Indeed,  the  qualities  of 
a  room,  in  regard  to  sound,  are  modified  by  so  many  circumstances, 
that  the  science  of  acoustics  is  worthy  of  more  attention  from  the 
architect  than  it  has  generally  received.  Plane  and  smooth  surfaces 
reflect  sound  without  dispersing  it,  convex  surfaces  disperse  it,  and 
concave  surfaces  Collect  it.  The  concentration  of  sound  by  concave 
surfaces,  produces  many  curious  effects  both  in  nature  and  art. 


REFLEXION    OF    SOUND.  187 

There  are  remarkable  situations  where  the  sound  from  a  cascade  is 
concentrated  by  the  surface  of  a  neighboring  cave,  so  completely, 
that  a  person  accidentally  bringing  his  ear  into  the  focus,  is  astound- 
ed by  a  deafening  noise.  Sound  issuing  from  the  center  of  a  circle, 
is,  by  reflexion,  returned  to  the  center  again,  producing  a  very  pow- 
erful echo.  Such  effects  are  observed  in  the  central  parts  of  a  cir- 
cular hall.  An  elliptical  apartment  conveys  sound  very  perfectly 
from  one  focus  to  the  other.  A  whisper  uttered  by  a  person  in  one 
focus  of  such  a  chamber,  will  be  audible  to  a  person  in  the  other 
focus,  though  not  heard  by  persons  between. 

361.  The  rolling  of  thunder  has  been  attributed  to  echoes  among 
the  clouds ;  and  that  such  is  the  case  has  been  ascertained  by  direct 
observation  on  the  sound  of  cannon.     Under  a  perfectly  clear  sky, 
the  explosion  of  guns  is  heard  single  and  sharp,  while,  when  the  sky 
is  overcast,  or  when  a  large  cloud  comes  over  head,  thp  reports  are 
accompanied   by  a  continued  roll,  like  thunder,  and  occasionally  a 
double  report  arises  from  a  single  shot.     The  continued  sound  of 
distant  thunder,  which  is  sometimes  prolonged  for  many  seconds,  is 
not  always  owing  to  reverberation,  but  frequently  arises  simply  from 
the  different  distances  of  the  same  flash.     Although  the  progress  of 
a  flash  of  lightning  through  the  air  were  absolutely  instantaneous, 
still,  if  its  path  were  in  a  line  that  would  carry  it  farther  from  the 
ear  in  one  place  than  in  another,  there  would  be  a  corresponding 
difference  in  the  times  at  which  the  sound  generated  in  different  por- 
tions of  the  path  would  reach  the  ear.     Herschel  observes,  that  if 
(as  is  almost  always  the  case)  the  flash  be  zigzag,  and  composed  of 
broken  rectilinear  and  curvilinear  portions,  some  concave,  some  con- 
vex to  the  ear ;  and  especially,  if  the  principal  trunk  separates  into 
many  branches,  each  breaking  its  own  way  through  the  air,  and  each 
becoming  a  separate  source  ef  thunder,  all  the  varieties  of  that  awful 
sound  are  easily  accounted  for. 

362.  The  Speaking  Trumpet  has  been  supposed  by  most  writers 
on  sound,  to  owe  its  peculiar  properties,  to  its  multiplying  sound  by  nu- 
merous reflexions.  Hence  is  suggested  the  form  of  a  parabolic  conoid, 
or  a  tube,  the  section  of  which  is  a  parabola,  the  place  of  the  mouth 
being  at  the  focus  of  the  parabola.    The  vibrations  emanating  from  the 


188  ACOUSTICS. 

mouth  would  then  be  reflected  into  straight  lines  parallel  with  the 
axis  of  the  trumpet,  and  would  thus  go  forward  in  a  collected  body 
to  a  distant  point.  And,  since  such  a  form  is  also  favorable  for  col- 
lecting distinct  sounds  into  one  point,  the  same  figure  is  proposed 
as  most  suitable  for  the  Ear  Trumpet.  But  the  sound  of  these  in- 
struments may  be  regarded  as  merely  the  longitudinal  vibration  of 
a  body  of  air,  to  which  momentum  is  given  in  the  direction  of  the 
axis,  not  by  reflexion  from  the  sides,  but  by  the  direct  impulse  of 
the  mouth.  The  ancients  were  acquainted  with  the  speaking  trum- 
pet. Alexander  the  Great  is  said  to  have  had  a  horn,  by  means  of 
which  he  could  give  orders  to  his  whole  army  at  once. 

363.  When  separate  sounds  are  repeated  with  a  certain  degree  of 
frequency,  the  ear  loses  the  power  of  distinguishing  the  intervals,  and 
they  appear  united  in  one  continued  sound.  By  this  means  also 
sounds  harsji  and  dissonant  in  themselves,  form  a  soft  and  agreeable 
tone.  Any  sound  whatever,  repeated  not  less  than  thirty  or  forty 
times  in  a  second,  excites  in  the  hearer  the  sensation  of  a  musical 
note.  Nothing  is  more  unlike  a  musical  sound  than  that  of  a  quill 
drawn  slowly  across  the  teeth  of  a  coarse  comb ;  but  when  the  quill 
is  applied  to  the  teeth  of  a  wheel  whirling  at  such  a  rate  that  720 
teeth  pass  under  the  quill  in  a  second,  a  very  soft,  clear  note  is 
heard.  In  like  manner  the  vibrations  of  a  long  harp-string,  while 
it  is  very  slack,  are  separately  visible,  and  the  pulses  produced  by  it 
in  the  air  are  separately  audible ;  but  as  it  is  gradually  tightened,  its 
vibrations  quicken,  and  the  eye  soon  sees,  when  it  is  moving,  only  a 
broad  shadowy  plane;  the  distinct  sounds  which  the  ear  lately  per- 
ceived, run  together,  owing  to  the  shortness  of  the  intervals,  and  are 
heard  as  one  uniform  continued  tone,  which  constitutes  the  note  or 
sound  proper  to  the  string. 

Nature  presents  us  with  numerous  examples  of  a  musical  sound 
produced  by  the  rapid  succession  of  an  individual  sound,  not  at  all 
musical  in  itself.  The  hum  of  winged  insects,  produced  by  the  fre- 
quent motion  of  their  wings,  the  murmur  of  a  forest  occasioned  by 
(he  agination  of  the  .leaves  and  boughs,  and  the  sublime  roar  of  the 
ocean  constituted  of  the  separate  sounds  produced  by  innumerable 
waves,  are  familiar  examples  of  the  operation  of  this  principle, 


PHILOSOPHICAL    PRINCIPLES    OF    MUSIC.  189 

364.  Musical  intervals,  or  sounds  differing  from  each  other  in 
pitch  by  a  certain  interval,  are  found  by^experience  to  be  peculiarly 
agreeable  to  the  human  ear,  a  fact  for  which  we  can  assign  no  reason 
except  that  such  is  the  constitution  of  the  mind.     Birds  may  some- 
times exhibit  a  fine  voice ;  but  their  singing  is  not  musical,  having 
nothing  to  do  with  musical  intervals. 

Musical  sounds  have  certain  ratios  to  one  another,  and  are  thus 
brought  into  the  province  of  Mathematics,  because  the  number  of 
vibrations  which  produce  one  musical  note,  has  a  constant  ratio  to 
the  number  which  produces  another  musical  note.  Thus,  if  we  di- 
minish the  length  of  a  musical  string  one  half,  we  double  the  num- 
ber of  its  vibrations  in  a  given  time,  and  it  gives  a  sound  eight  notes 
higher  in  the  scale  than  that  given  by  the  whole  string.  Therefore, 
these  sounds  are  represented  by  the  numbers  2  and  1,  and  are  said 
to  be  in  the  ratio  of  2  to  1.  The  upper  note  is  said  to  be  the  octave 
of  the  lower ;  and  from  its  great  resemblance  to  the  fundamental 
note,  or  that  afforded  by  the  whole  string,  it  is  considered  as'the 
commencement  of  a  repetition  of  the  same  series ;  so  that  all  audi- 
ble sounds  are  considered  as  repetitions  of  a  series  contained  within 
the  interval  of  an  octave. 

365.  A  succession  of  single  musical  sounds,   constitutes  melody ; 
the  combination  of  such  sounds,   at  proper  intervals,   forms  chords ; 
and  a  succession  of  chords  constitutes  harmony.     Two  notes  pro- 
duced by  an  equal  number  of  vibrations  in  a  given  time,  and  of  course 
giving  the  same  sound,   are  said  to  be  in  unison.     The  relation  be- 
tween a  note  and  its  octave  is,  next  after  that  of  the  unison,  the  most 
perfect  in  nature ;  and  when  the  two  notes  are  sounded  at  the  same 
time,  they  almost  entirely  unite.     Chords  are  characterized  by  fre- 
quent coincidences  of  vibration,  while  in  the  discords  such  coinci- 
dences are  more  rare.     Thus  injunison,  the  vibrations  are  perfectly 
isochronous ;  in  the  octave  the  two  coincide  at  the  end  of  every  vi- 
bration of  the  longer  string,  the  shorter  meanwhile  performing  just 
two  vibrations ;  and  in  the  fifth,  they  coincide  at  the  end  of  every 
two  vibrations  of  the  longer  string,  the  shorter  vibrating  three  limes 
in  the  same  period.     But  in  the  second,  the  longer  and  shorter  vi- 
brations can  coincide  only  after  eight  of  the  longer  and  nine  of  the 
shorter,  and  in  the  seventh,  only  after  eight  of  the  longer  and  fifteen 


190  ACOUSTICS. 

of  the  shorter.     Hence  the  concord  is  more  perfect  as  the  common 
period  is  shorter. 

Musical  intervals  therefore  are  divided  into  chords  and  discords. 
The  octave,  the  major  fifth,  the  major  and  minor  thirds,  the  major 
and  minor  sixths,  are  concords,  and  are  pleasing  in  themselves.  The 
seconds,  the  sevenths,  the  minor  fifth  and  major  fourths,  are  discords. 
The  chord  consisting  of  the  fundamental  note  with  its  third  and  fifth, 
and  called  the  harmonic  triad,  forms  the  most  perfect. harmony,  and 
contains  the  constituent  parts  of  the  most  simple  and  natural  melo- 
dies. 

366.  Discords,  however,  are  employed  in  musical  compositions; 
but  their  use  is  limited  by  special  rules.     Of  the  occasion  and  man- 
ner of  introducing  them,  the  following  extract  from  Burney's  History 
of  Music,   will  give  the  learner  a  general  idea.     "  While  harmony 
was  refining  and  receiving  new  combinations,  it  was  found,  like  other 
sweet  and  luscious  things  to  want  qualification  to  keep  off  languor 
and  satiety,  when  some  bold  musician  had  the  courage  and  address 
to  render  it  piquant  and  interesting,  by  means  of  discords,  in  order 
to  stimulate  attention ;  and  thus  by  giving  the  ear  a  momentary  un- 
easiness, and  keeping  it  in  suspense,  its  delight  became  the  more  ex- 
quisite, when  the  discordant  difficulty  was  solved.     Discord  in  mu- 
sical composition,  however,  does  not  consist  in  the  excess  or  defect 
of  intervals,  which,  when  false,  produce  jargon,  not  music;  but  in  the 
warrantable  and  artful  use  of  such  combinations  as,  though  too  disa- 
greeable for  the  ear  to  dwell  upon,  or  to  firnish  a  musical  period,  yet 
so  necessary  are  they  to  modern  counterpoint,  and  modern  ears,  that 
harmony  without  their  relief,   would  satiate,   and  lose  many  of  its 
beautiful  effects." 

367.  The  theory  of  Musical  Instruments  will  be  readily  under- 
stood from  the   principles  already  explained.     It  will  be  seen   thai 
they  all  owe  their  power  of  producing  musical  sounds  to  their  sus- 
ceptibility of  vibrations ;  that  the  force  or  loudness  of  the  sounds 
they  afford  depends  on  the  length  of  the  vibrations,  and  the  gravcness 
or  acuteness  of  the  sound,   in  other  words  the  pitch,   on  their  slow- 
ness or  frequency ;  an/1  that  their  chords  depend,   in  general,    upon 
frequency  of  coincidence  in  the   vibrations  that  afford  the  several 


PHILOSOPHICAL  PRINCIPLES  OF  MUSIC. 

sounds  of  the  concord.  The  nature  of  stringed  instruments  may 
be  learned  from  the  violin.  Here  the  strings  are  of  the  same  length, 
but  differ  in  weight  and  tension ;  those  designed  to  afford  the  lower 
notes  being  heavier  and  less  strained,  and  those  for  the  higher  notes 
being  lighter  and  more  tense.  The  lengths,  moreover,  are  altered  by 
applying  the  fingers.  The  several  strings  are  usually  so  adjusted  to 
each  other,  that  is,  so  tuned,  that  any  two  contiguous  strings  make  a  t 
fifth.  Hence  the  fourth  or  highest  stop  on  one  string  brings  it  into 
unison  with  the  string  above ;  and  the  third  stop  on  any  string  forms 
an  octave  with  the  open  string  next  below.  On  account  of  this  power 
of  altering  the  effective  lengths  of  the  strings  at  pleasure,  of  devel- 
oping the  harmonic  sounds  by  a  skilful  application  of  the  fingers,  and 
of  varying  constantly  the  degrees  of  fullness  or  force  in  each  sound 
by  a  dexterous  use  of  the  bow,  the  violin  becomes,  in  the  hands  of 
an  accomplished  performer,  an  instrument  of  great  power  and  com- 
pass, while  it  is  capable  of  greater  variety  than  any  other  musical 
instrument. 

The  flute  affords  'an  example  of  wind  instruments.  Here  the 
vibrating  body  is  a  column  of  air  to  which  different  lengths  are  given 
by  means  of  the  stops  which  are  opened  and  closed  by  the  fingers. 
The  rapidity  of  the  vibrations,  and  consequently  the  pitch,,  is  also 
changed  a  whole  octave  by  the  management  of  the  breath* 

3C8;  In  mixed  wind  instruments,  the  vibrations  or  alternations  of 
solid  bodies  are  made  to  cooperate  with  the  vibrations  of  a  given  por- 
tion of  air.  Thus,  in  the  trumpet,  and  in  horns  of  various  kinds,  the 
force  of  inflation,  and  perhaps  the  degree  of  tension  of  the  lips,  de- 
termines the  nnmber  of  parts  into  which  the  tube  is  divided,  and  the 
harmonic  which  is  produced.  The  hautboy  and  clarionette  have 
mouth-pieces  of  different  forms,  made  of  reeds  or  canes ;  and  the 
reed-pipes  of  an  organ,  of  various  constructions,  are  furnished  with 
an  elastic  plate  of  metal,  which  vibrates  in  unison  with  the  column 
of  air  which  they  contain.  An  organ  generally  consists  of  a  number 
of  different  series  of  pipes,  so  arranged,  that,  by  means  of  registers, 
the  air  proceeding  from  the  bellows  may  be  admitted  to  supply  each 
series,  or  excluded  from  it  at  pleasure ;  and  a  valve  is  opened  when 
the  proper  key  is  touched,  which  causes  all  the  pipes  belonging  to 
the  note,  in  those  series  of  which  the  registers  are  open,  to  sound 
at  once. 


192 


PART  IV. ELECTRICITY. 

CHAPTER  1, 

OF  THE  GENERAL  PRINCIPLES  OF  THE  SCIENCE. 

369.  The  term  ELECTRICITY  is  used  to  denote  both  the  unknown 
cause  of  electrical  phenomena,  and  the  science  which  treats  of  elec- 
trical phenomena  and  their  causes. 

The  most  general  effect  by  which  the  presence  of  electricity  is 
manifested  is  attraction.  Thus,  when  a  glass  tube  is  rubbed  with  a 
dry  silk  or  woollen  cloth,  it  acquires  the  property  of  attracting  light 
bodies,  as  cotton,  feathers,  &ic.  When,  by  any  process,  a  body  is 
made  to  give  signs  of  electricity,  it  is  said  to  be  excited.  When  a 
body  receives  the  electric  fluid  from  an  excited  body,  it  is  said  to  be 
electrified.  Since  there  is  found  to  be  a  greater  difference  in  bodies 
in  regard  to  the  power  of  transmitting  electricity,  all  bodies  are  divi- 
ded into  two  classes  CONDUCTORS  and  NON-CONDUCTORS.  Conduc- 
tors are  bodies  through  which  the  electric  fluid  passes  readily  ;  non- 
conductors are  bodies  through  which  the  electric  fluid  either  does 
not  pass  at  all,  or  but  very  slowly.  The  latter  bodies  are  also  de- 
nominated electrics,  because  it  is  by  the  friction  of  bodies,  of  this 
class  that  electricity  is  usually  excited.  An  electrified  body  is  said 
to  be  insulated^  when  its  connexion  with  other  bodies  is  formed  by 
means  of  non-conductors,  so  that  its  electricity  is  prevented  from 
escaping.  Instruments  employed  to  detect  the  presence  of  electri- 
city are  denominated  electroscopes;  such  as  are  employed  to  estimate 
its  comparative  quantity,  are  called  electrometers.  This  distinction, 
however,  is  neglected  by  some  writers,  and,  to  avoid  the  unneces- 
sary multiplication  of  terms,  it  will  be  neglected  in  the  present  trea- 
tise, instruments  of  either  kind  being  called  electrometers. 

370.  The  Pendulum  Electrometer  is  formed  by  suspending  some 
light  conducting  substance  by  some  non-conducting  substance.    Thus, 
a  small  ball  of  the  pith  of  elder  hung  by  a  silk  thread,  constitutes  a 


GENERAL    PRINCIPLES. 


Fig.  78, 


very  convenient  instrument  for  detecting  the  presence  and  examining 
the  kind  of  electricity.  Figure  78,  represents  a  pen- 
dulum electrometer,  consisting  of  a  glass  rod  fixed  in 
a  stand,  and  bent  at  the  top  so  as  to  form  a  hook. 
From  this  hook  hangs  a  thread  of  raw  silk,  to  the  bot- 
tom of  which  is  attached  a  small  pith  ball,  made 
smooth  and  round,  and  weighing  only  a  small  part  of 
a  grain.  The  attenuated  thread  of  silky  unwound 
from  the  ball  of  the  silk  worm,  forms  a  very  delicate 
insulator;  but  for  ordinary  purposes,  a  common  thread 
of  silk  may  be  untwisted,  and  a  single  filament  taken 
for  the  suspending  thread.  For  the  purposes  of  the 
learner,  it  may  even  be  sufficient  to  suspend  a  ball  of 
cork,  or  a  lock  of  cotton,  or  a  feather  by  a  thread  of 
silk.  The  Gold  Leaf  Electrometer,  represented  in 
Fig.  79,  consists  of  two  strips  of  gold  leaf  suspend- 
ed from  the  metallic  cover  of  a  small  glass  cylinder. 
By  this  arrangement,  the  pieces  of  gold  leaf  are  insu- 
lated, they  are  protected  from  agitation  by  the  air,  and 
Electricity  is  easily  conveyed  to  them  by  bringing  an 
electrified  body  into  contact  with  the  cover.  The 
approach  of  an  electrified  body  causes  the  leaves  to 
separate,  or  when  previously  separated,  to  collapse 
according  to  principles  to  be  explained  presently. 

By  the  aid  of  the  foregoing  instruments,  or  even  by  means  of 
the  pendulum  electrometer  alone,  we  may  ascertain  the  following 
LEADING  FACTS,  which  are  so  many  fundamental  truths,  in  the  sci- 
ence of  Electricity. 

371.  PROP.  I.  Electricity  is  produced  by  the  Friction  of  all 
bodies. 


Fig.  79, 


Although  friction  is  the  most  common  and  by  far  the  most  exten- 
sive means  of  exciting  bodies,  yet  it  is  not  the  only  means.  Elec- 
tricity is  manifested  during  the  changes  of  state  in  bodies,  such  as 
liquefaction  and  congelation,  evaporation  and  condensation.  Some 
bodies  even  are  excited  by  mere  pressure ;  others  by  the  contact  or 
separation  of  different  surfaces.  Most  chemical  combinations  and 

25 


194  ELECTRICITY. 

decompositions  are   also  attended  by   the   evolution  of  Electricity 
which  manifests  its  presence  to  delicate  electrometers. 

If  we  rub  a  piece  of  amber,  sealing  wax,  or  any  other  resinous  sub- 
stance on  dry  wollen  cloth,  or  fur,  or  silk,  and  bring  it  towards  an  elec- 
trometer, it  will  give  signs  of  electricity.  A  glass  tube  may  be  exci- 
ted in  a  similar  manner.  Moreover  if  we  bring  the  excited  tube  near 
the  face,  it  imparts  a  sensation  resembling  that  produced  by  a  cobweb. 
If  the  tube  is  strongly  excited,  it  will  afford  a  spark  to  the  knuckle, 
accompanied  by  a  snapping  noise.  A  sheet  of  white  paper,  first 
dried  by  the  fire,  and  then  laid  on  a  table  and  rubbed  with  India 
rubber,  will  become  so  highly  excited  as  to  adhere  to  the  wall  of 
the  room,  or  any  other  surface  to  which  it  is  applied.  Indeed  fric- 
tion is  so  constantly  attended  by  Electricity,  that  in  favorable  weath- 
er the  fluid  is  abundantly  indicated  on  brushing  our  clothes,  which 
thus  are  made  to  attract  the  light  downy  particles  that  are  floating 
in  the  air. 

372.  Our  proposition  asserts  that  Electricity  is  produced  by  the 
friction  of  all  bodies,  whereas  if  we  hold  in  the  hand  a  metallic  sub- 
stance, a  plate  of  brass  or  iron,  for  example,  and  subject  it  to  friction, 
we  shall  not  discover  the  least  sign  of  electrical  excitement.     In  such 
cases,  however,  the  Electricity  is  prevented   from  accumulating  in 
consequence  of  the  substance  being  a  good  conductor,  and  thus  con- 
veying the  fluid   to  the  hand,  which  is  another  good  conductor,   by 
which  means  it  is  lost  as  fast  as  it  is  excited.     But  if  we  insulate  a 
metallic  body,   or  any  other  conducting  substance,  then  on  being 
rubbed,  it  gives  signs  of , Electricity,  like  electrics. 

373.  PROP.  II.   The  Electricity  which  is  excited  from  GLASS  and 
a  numerous  class  of  bodies,   exhibits  different  properties  from  that 
which  is  excited  from  AMBER,   or  sealing  wax,  and  a  class  of  bodies 
equally  numerous  with  the  other. 

The  kind  of  fluid  excited  from  glass  and  analogous  bodies  is  called 
vitreous,  and  that  from  amber  and  analogous  bodies,  resinous  Elec- 
tricity. .-/The  term  positive  is  also  used  instead  of  vitreous,  and  negp- 
•  twe  instead  of  resinous. 

In  order  to  understand  the  applications  of  the  preceding  terms 
vitreous  and  resinous,  positive  and  negative,  it  is  necessary  to  know 


GENERAL    PRINCIPLES.  195 

something  of  the  two  hypotheses  upon  which  these  terms  are  respec- 
tively founded.  The  first  hypothesis  is  that  proposed  by  Du  Fay. 
It  ascribes  all  electrical  phenomena  to  the  agency  of  two  fluids  spe- 
cifically different  from  each  other,  and  pervading  all  bodies.  In  un- 
electrified  bodies,  these  two  fluids  exist  in  combination,  and  exactly 
neutralize  each  other.  By  the  separation  of  the  two  fluids  it  is 
that  bodies  are  electrified,  and  it  is  by  the  re-union  of  the  two  fluids, 
that  the  Electricity  is  discharged,  or  bodies  cease  to  be  excited.  The 
second  hypothesis  was  proposed  by  Dr.  Franklin.  It  ascribes  all 
electrical  phenomena  to  the  agency  of  one  fluid,  which,  as  in  the 
other  case  is  supposed  to  pervade  all  bodies,  being  naturally  in  a  state 
of  equilibrium.  It  is  only  when  this  equilibrium  is  destroyed  that 
bodies  become  electrified,  and  it  is  by  the  restoration  of  the  equi- 
librium that  the  Electricity  is  discharged,  or  bodies  cease  to  be  ex- 
cited. But  a  body  is  electrified  when  it  has  either  more  or  less 
of  the  fluid  tha'n  its  natural  share ;  in  the  former  case  it  is  positive- 
ly, in  the  latter  case  negatively,  electrified ;  positive  Electricity  there- 
fore, implies  a  redundancy,  and  negative  Electricity,  a  deficiency  of 
the  fluid. 

374.  PROP.  III.  Bodies  electrified  in  different  ways  attract,  and 
in  the  same  way  repel  each  other. 

Thus,  if  an  insulated  pith  ball,  (Art.  370.)  or  a  lock  of  cotton,  be 
electrified  by  touching  it  with  an  excited  glass  tube,  it  will  immedi- 
ately recede  from  the  tube,  and  from  all  other  bodies  which  afford 
the  vitreous  Electricity,  while  it  will  be  attracted  by  excited  sealing 
wax,  and  by  all  other  bodies  which  afford  the  resinous  Electricity. 
If  a  lock  of  fine,  long  hair  be  held  at  one  end,  and  brushed  with  a 
dry  brush,  the  separate  hairs  will  become  electrified,  and  will  repel 
each  other.  In  like  manner,  two  insulated  pith  balls,  or  any  other 
light  bodies  will  repel  each  other  when  they  are  electrified  the  same 
*way,  and  attract  each  other  when  they  are  electrified  different  ways. 

Hence  it  is  easy  to  determine,  whether  the  Electricity  afforded  by 
a  given  body  is  vitreous  or  resinous;  for,  having  electrified  the  elec- 
trometer by  excited  glass,  then  all  those  bodies  which,  when  exci- 
ted, attract  the  ball,  afford  the  resinous,  while  all  those  which  repel 
the  ball  afford  the  vitreous  Electricity, 


196  ELECTRICITY. 

375.  PROP.  IV.   The  two  kinds  of  Electricity  are  produced  simul- 
taneously ;  the  one  kind  in  the  body  rubbed,  the  other  in  the  rubber. 

For  example,  if  we  rub  a  glass  tube  with  a  silk  or  woollen  cloth, 
the  glass  becomes  positive,  and  the  cloth  negative.  The  foregoing 
Jaw  holds  true  universally ;  but  the  kind  of  Electricity  which  each 
substance  acquires,  depends  upon  the  substance  against  which  it  is 
rubbed.  If  we  rub  dry  woollen  cloth  against  smooth  glass,  it  ac- 
quires the  resinous,  and  the  glass,  the  vitreous  Electricity ;  but  if 
we  rub  the  same  cloth  against  rough  glass,  it  becomes  positively, 
while  the  glass  becomes  negatively,  electrified.  The  following  table 
contains  a  number  of  electric  substances,  arranged  in  such  a  way  that 
when  they  are  rubbed  against  each  other,  any  substance  in  the  list  be- 
fore another  becomes  positively,  and  any  substance  below  it,  nega- 
tively, electrified. 

1.  Fur  of  a  Cat,  6.  Paper, 

2.  Smooth  Glass,  7.  Silk, 

3.  Woollen  Cloth,  8.  Lac,      ,  • 

4.  Feathers,  9.  Rough  Glass, 

5.  Wool,  10.  Sulphur. 

The  fur  of  a  cat,  when  rubbed  against  any  of  the  bodies  in  the  table, 
always  affords  the  vitreous,  and  the  sulphur  always  the  resinous  elec- 
tricity. Feathers  become  negative  when  rubbed  against  the  fur  of  a 
cat,  smooth  glass,  or  woollen  cloth;  but  positive  when  rubbed  against 
wool,  paper,  silk,  lac,  rough  glass,  or  sulphur. 

376.  PROP.  V.  Electricity  passes  through  some  bodies  with  the. 
greatest  facility  ;  through  others  with  the  greatest  apparent  difficul- 
ty >  or  scarcely  at  all ;  and  others  have  a  conducting  power  interme- 
diate between  the  two. 

Metals  and  charcoal,  water  and  all  liquids  (oils  excepted)  are  good 
conductors.  Melted  wax  and  tallow  are  good  conductors  ;  but  these 
bodies  while  solid  conduct  very  badly.  Glass,  resins,  gums,  sealing 
wax,  silk,  sulphur,  precious  stones,  oxides,  air,  and  all  gases,  are  non- 
conducfeo,rs,  or  at  least  very  bad  conductors.  Atmospheric  air  is  a 
non-conductor  of  the  highest  class,  when  perfectly  dry ;  but  it  be- 
comes a  conductor,  either  when  moist  or  when  rarefied.  The  elec- 
tric fluid  easily  pervades  the  vacuum  of  an  air  pump,  or  of  the  Torn- 


GENERAL    PRINCIPLES.  197 

cellian  tube ;  but  these  are  imperfect  vacuums ;  it  is  said  that  Elec- 
tricity cannot  pass  through  a  perfect  vacuum.  The  conducting  pow- 
ers of  most  bodies  are  influenced  by  changes  of  temperature,  and 
also  by  changes  of  form.  Water,  in  its  natural  state,  is  a  good  con- 
ductor 5  but  its  conducting  power  is  increased  by  heat  and  diminish- 
ed by  cold. 

The  same  body  frequently  exhibits  great  changes  in  conducting 
power  by  changes  of  state,  or  chemical  constitution.  Thus,  green 
wood  is  a  conductor,  dry  baked  wood  a  non-conductor ;  charcoal  a 
conductor,  ashes  a  non-conductor.  It  is  particularly  important  to 
remember  that  Metals,  Water  and  all  moist  substances,  Animal  sub- 
stances, as  the  human  body,  and  the  Earth  itself,  are  conductors ; 
while  the  Air,  when  dry,  and  all  Resinous  and  Vitreous  substances 
are  non-conductors.  These  bodies  are  those  which  are  chiefly  con- 
cerned in  making  experiments  with  electrical  apparatus. 

377.  PROP*.  VI.  Insulation  is  effected  in  various  degrees  of  per- 
fection, according  to  the  state  of  the  atmosphere,  and  the  nature  of 
the  substances  employed  as  insulators. 

If  the  air  were  a  conductor,  it  is  not  easy  to  see  how  the  electric 
fluid  could  be  confined  so  as  to  be  accumulated.  It  is,  moreover, 
only  when  the  air  is  dry  that  it  is  capable  of  insulating  well ;  hence, 
in  damp,  foggy  and  rainy  weather,  electrical  apparatus  will  not  work 
well,  unless  the  air  is  dried  artificially  by  operating  in  a  close  room 
highly  heated  by  a  stove.  Lac,  drawn  into  fine  threads,  is  the  most 
perfect  insulator.  Compared  with  silk  thread,  such  a  filament  is  ten 
times  more  effectual  in  preventing  the  loss  of  the  fluid.  Fine  silk 
thread,  however,  when  perfectly  dry,  is  among  the  best  insulators, 
and  where  great  delicacy  is  required,  a  single  filament  of  silk  as  it 
comes  from  the  ball  of  the  silk  worm  is  employed.  Its  conducting 
power  is  somewhat  influenced  by  its  color,  black  being  the  worst, 
and  a  gold  yellow  the  best  color  for  insulating.  Glass  is  much  used 
as  an  insulator,  especially  when  great  strength  is  required,  as  in  sup- 
ports to  various  kinds  of  electrical  apparatus.  Glass,  however,  is 
liable  to  acquire  moisture  on  its  surface,  in  consequence  of  which  its 
properties  as  an  insulator  are  materially  impaired.  This  inconven- 
ience is  obviated  by  giving  it  a  thick  coat  of  varnish.  Fine  hair  is  a 
good  and  convenient  substance  in  some  cases  of  insulation. 


198  ELECTRICITY. 

In  some  cases,  conducting  or  uninsulating  threads  are  required. 
Then  fine  silver  wires,  or  linen  threads  first  steeped  in  a  solution  of 
salt  and  dried,  are  used. 

378.  The  sphere  of  communication  is  the  space  within  \vhich  a 
spark  may  pass   from  an  electrified   body,  in  any  direction  from  it. 
It  is  sometimes  called  the  striking  distance.     The  sphere  of  influence 
is  the  space  within  which  the  power  of  attraction  of  an  electrified 
body  extends  in  every  way,   beyond  the  sphere  of  communication. 
A  glass  tube  strongly  excited  will  exert  an  influence  upon  the  gold 
leaf  electrometer  at  the  distance  of  ten  or  even  twenty  feet,  although 
a  spark  could  not  pass  from  the  tube  to  the  cap  of  the  electrometer 
at  a  greater  distance  than  a  few  inches. 

379.  The  electricity  which  a  body  manifests  by  being  brought  near 
to  an  excited  body,  without  receiving  a  spark  from  it,  is  said  to  be 
acquired  by  Induction. 

When  an  insulated  conductor,  unelectrified,  is  brought  into  the 
neighborhood  of  an  insulated  charged  conductor,  its  Electricity  un- 
dergoes a  new  arrangement.  The  end  of  it  next  to  the  excited 
conductor,  assumes  a  state  of  electricity  opposite  to  that  of  the  ex- 
cited conductor ;  while  the  farther  extremity  assumes  the  same  kind 
of  electricity.  Suppose  the  excited  conductor  is  electrified  positive- 
ly. The  end  of  the  insulated  conductor  next  to  it,  becomes  negative, 
and  the  remoter  end  positive ;  and  intermediate  between  these  two 
points,  there  occurs  a  place  where  neither  positive  nor  negative  elec- 
tricity can  be  perceived.  This  place  is  called  the  neutral  point. 

The  reason  why  unelectrified  bodies  are  attracted  by  excited  elec- 
trics is,  that  they  are  put  into  the  opposite  state  by  induction,  and 
then  attracted  upon  the  general  principle  laid  down  in  Prop.  III. 
When  they  come  into  the  sphere  of  communication  of  the  excited 
body,  they  immediately  acquire  the  same  kind  of  electricity,  and  are 
repelled.  If  they  come  into  contact  with  uninsulated  bodies  they 
lose  the  electricity  they  have  acquired,  are  again  put  into  the  opposite 
state  byjnduction,  again  attracted  and  again  repelled.  This  process 
will  go  on  until  the  electricity  of  the  insulated  conductor  is  all  con- 
veyed away. 


ELECTRICAL    APPARATUS.  199 

The  foregoing  general  principles  may  be  verified  with  very  sim- 
ple apparatus  such  as  pith  balls,  a  glass  tube,  and  a  stick  of  seal- 
ing wax.  But  the  same  facts  may  be  exhibited  in  a  much  more 
striking  and  impressive  manner  by  the  electrical  machine  and  its  ap- 
pendages, and  our  attention  will  therefore  be  now  turned  to  the  con- 
sideration of  the  subject  of  electrical  apparatus. 


CHAPTER  II. 

OF  ELECTRICAL  APPARATUS. 

380.  The  object  of  the  electrical  machine  is  to  accumulate  elec- 
tricity. It  is  made  of  several  different  forms,  but  two  of  these  forms 
are  predominant,  which  it  will  be  sufficient  for  our  present  purpose 
to  describe ;  of  these  one  is  called  the  Cylinder,  the  other,  the  Plate 
machine.  The  CYLINDER  MACHINE  is  represented  in  figure  80. 

Fig.  80. 


The  principal  parts  belonging  to  it,  are  the  cylinder,  the  frame,  the 
rubber,  and  the  prime  conductor.  The  cylinder  (A)  is  of  glass, 
from  eight  to  twelve  incbes  in  diameter,  and  from  twelve  to  twenty 
four  inches  long.  It  should  be  perfectly  cylindrical,  otherwise  it 
will  not  press  the  cushion  or  rubber  evenly  when  turned.  It  must  be 
as  smooth  as  possible,  for  rough  glass  becomes  a  partial  conductor. 


200  ELECTRICITY. 

The  cylinder  should  be  so  mounted  on  the  frame  as  to  revolve  without 
waddling,  for  such  a  motion  would  prevent  its  being  in  uniform  contact 
with  the  rubber.  The  Frame  (B  B)  is  made  of  wood,  which  must 
be  close  grained,  well  seasoned,  and  baked  in  an  oven,  and  finally 
coated  with  varnish,  the  object  of  all  this  preparation  being  to  dimin- 
ish its  conducting  powers,  and  thus  preveBt  its  wasting  the  electricity 
of  the  cylinder.  The  Rubber  (C,)  consists  of  a  leathern  cushion, 
stuffed  with  hair  like  the  padding  of  a  saddle.  This  is  covered  with 
a  black  silk  cloth,  having  a  flap  which  extends  from  the  cushion  over 
the  top  of  the  cylinder  to  the  distance  of  an  inch  from  the  points  con- 
nected with  the  prime  conductor,  to  be  mentioned  presently.  The 
rubber  is  coated  with  an  amalgam*  made  of  mercury,  zinc,  and  tin, 
which  preparation  has  been  found,  by  experience,  to  produce  a  high 
degree  of  electrical  excitement,  when  subjected  to  the  friction  of 
glass.  The  rubber  is  insulated  by  placing  it  on  a  solid  glass  pillar, 
and  it  is  made  to  fit  closely  to  the  cylinder  by  means  of  a  spring 
worked  by  a  screw. 

The  Prime  Conductor  D,  is  usually  a  hollow  brass  cylinder  with 
hemispherical  ends.  It  is  mounted  on  a  solid  glass  pillar,  with  a 
broad  and  heavy  foot  made  of  wood  to  keep  it  steady.  The  cylin- 
der is  perforated  with  small  holes,  for  the  reception  of  wires  (c)  with 
brass  knobs. 

It  is  important  to  the  construction  of  an  electrical  machine,  that 
the  work  should  be  smooth  and  free  from  points  and  sharp  edges* 


*  The  amalgam  recommended  by  Singer,  one  of  the  ablest  practi- 
cal electricians,  is  composed  of  zinc  two  ounces,  of  tin  one  ounce, 
and  of  mercury  six  ounces.  The  zinc  and  tin  may  be  melted  together 
in  a  ladle  or  crucible,  and  poured  into  a  mortar,  previously  heated 
to  prevent  the  sudden  congelation  of  the  melted  metals.  As  soon  as 
they  are  introduced,  they  mast  be  rapidly  stirred  with  the  pestle,  du- 
ring which  process  the  mercury  may  be  added,  and  the  stirring  con- 
tinued until  the  amalgam  is  cold,  when  it  will  be  in  the  form  of  paste 
or  fine  powder.  A  little  lard  is  added,  to  give  the  amalgam  the  prop- 
er consistence ;  but  if,  when  applied,  it  be  warmed  a  little,  but  a  small 
proportion  of  lard  need  be  used.  In  hot  weather,  less  quicksilver  is 
to  be  employed. 


ELECTRICAL    APPARATUS. 


201 


since  these  have  a  tendency  to  dissipate  the  fluid,  as  will  be  more  fully 
understood  hereafter.  For  a  similar  reason  the  machine  should  be 
kept  free  from  dust,  the  particles  of  which  act  like  points,  and  dissi- 
pate the  electricity. 

381.  The  PLATE  MA- 
CHINE  (Fig.  81.)  con- 
sists of  a  circular  plate 
of  glass  from  eight- 
een to  twenty  four  inch- 
es or  more  in  diameter, 
turning  vertically  on  an 
axis  that  passes  through 
its  center.  The  frame 
is  composed  of  materi- 
als similar  to  those 
which  compose  the 
frame  of  the  cylindri- 
cal machine.  This  ma- 
chine is  furnished  with 
two  pairs  of  rubbers, 
attached  to  the  top  and 
bottom  of  the  plate. 
The  prime  conductor  consists  of  a  brass  cylinder,  proceeding  from 
the  center  in  a  line  with  the  axis,  and  having  two  branches  which 
serve  to  increase  its  surface,  and  at  the  same  time  to  connect  it  with 
the  opposite  sides  of  the  plate,  so  as  to  receive  the  Electricity  as  it  is 
evolved  from  each  cushion. 

It  is  not  agreed  which  of  these  two  machines  affords  the  greatest 
quantity  of  Electricity  from  the  same  surface ;  but  the  cylinder  is 
less  expensive  than  the  plate,  and  less  liable  to  break,  and  is  more 
convenient  for  common  use. 

382.  The  principles  of  the  electrical  machine,  will  be  readily 
comprehended  from  what  has  gone  before.  It  differs  from  the  glass 
tube,  only  in  affording  a  more  convenient  and  effectual  mode  of  pro- 
ducing friction.  By  the  friction  of  the  glass  cylinder  or  plate  against 
the  rubber,  electricity  is  evolved,  which  is  immediately  transferred  to- 
the  prime  conductor,  and  may  be  taken  from  the  latter  by  the  knuek- 

26 


202  ELECTRICITY. 

le,  or  any  other  conducting  substance.  If  the  glass  and  rubber  both 
remain  insulated,  the  quantity  of  Electricity  which  they  are  capable 
of  affording,  will  soon  be  exhausted.  Hence,  a  chain  or  wire  is 
hung  to  the  rubber  and  suffered  to  fall  upon  the  table  or  the  floor, 
which,  communicating  as  it  does  with  the  walls  of  the  building,  and 
finally  with  the  earth,  supplies  an  inexhaustible  quantity  of  the  fluid 
to  the  rubber.  In  cases  where  very  great  quantities  of  electricity  are 
required,  a  metallic  communication  may  be  formed  immediately  be- 
tween the  rubber  and  the  ground.* 

383.  In  order  to  indicate  the  degree  of  excitement  in  the  prime 
conductor,  the  Quadrant  Electrometer  is  attached  to  it,  as  is  repre- 
sented at  E  in  Fig.  80.  This  electrometer  is  formed  of  a  semicir- 
cle, usually  of  ivory,  divided  into  degrees  and  minutes,  from  0  to 
180, •(•  the  graduation  beginning  at  the  bottom  of  the  arc.  The  in- 
dex consists  of  a  straw,  moving  on  the  center  of  the  disk,  and  carry- 
ing, at  the  other  extremity,  a  small  pith  ball.  The  perpendicular 
support  is  a  pillar  of  brass,  or  some  conducting  substance.  When 
this  instrument  is  in  a  perpendicular  position  and  not  electrified,  the 

*  As  electrical  machines  are  expensive,  and  not  always  easily  pro- 
cured by  the  private  learner,  it  may  be  useful  to  suggest  a  mode  of 
fitting  up  a  cheap  apparatus.  A  large  tincture  bottle  may  be  procured 
of  the  apothecary,  for  the  cylinder.  A  cover  of  wood  may  be  ce- 
mented to  each  end,  to  the  center  of  which,  next  to  the  bottom,  is 
screwed  a  projecting  knob  for  one  end  of  the  axis,  while  the  part  of 
the  axis  to  which  the  handle  is  attached,  is  screwed  into  the  center  of 
the  cover  of  wood  next  to  the  nozzle.  Thus  prepared,  it  may  be 
mounted  on  such  a  frame  of  hard  dry  wood  as  every  joiner  or  cabinet 
maker  can  construct.  A  tinner  can  make  the  prime  conductor,  and 
several  other  appendages  to  be  described  hereafter.  Junk  bottles  or 
long  vials  servo  well  as  insulators.  Ingenious  students  of  electricity, 
frequently  amuse  themselves  with  making  machines  of  this  description, 
some  of  which  have  answered  nearly  every  purpose  of  the  most  ex- 
pensive Jkinds  of  apparatus. 

A  cement,  for  electrical  purposes,  maybe  made  by  melting  together 
five  ounces  of  resin,  one  ounce  of  beeswax,  one  ounce  of  Spanish 
brown,  and  a  tea  spoonful  of  plaster  of  Paris,  or  brick  dust. 

t  Sometimes  the  division  is  carried  only  to  90°,  which  is  all  that  is 
necessary. 


ELECTRICAL    APPARATUS.  203 

index  hangs  by  the  side  of  the  pillar,  perpendicularly  to  the  horizon ; 
but  when  the  prime  conductor  is  electrified,  it  imparts  the  same  kind 
of  electricity  to  the  index,  repels  it,  and  causes  it  to  rise  on  the  scale 
towards  an  angle  of  90°,  or  to  a  position  at  right  angles  with  the 
pillar. 

384.  When  an  electrical  machine  is  skillfully  fitted  up,  and  works 
well,  on  turning  it,  circles  of  light  surround  the  cylinder  or  plate,  and 
brushes  or  pencils  of  light  emanate  copiously  from  the  cushion  and 
other  parts  of  the  machine.     The  circles  of  light  consist  of  electric 
sparks,  which  discharge  themselves  between  the  excited  surface,  and 
the  rubber,  their  passage  being  so  rapid  as  to  appear  like  a  continued 
line,  like  that  of  a  small  stick  ignited  at  the  end  and  whirled  in  the 
air.     The  brushes  of  light  arise  from  the  facility  with  which  the  fluid 
escapes  from  points  or  thin  edges. 

The  experiments  which  were  previously  performed  on  electrical 
attractions  and  repulsions,  (Arts.  369 — 376.)  may  now  be  repeated 
in  a  much  more  striking  manner,  and  various  other  experiments  add- 
ed, which  can  be  shown  only  when  electricity  is  accumulated. 

385.  We  proceed  to  enumerate  a  few  of  the  effects  of  electricity 
as  they  are  exhibited  by  the  electrical  machine,  confining  ourselves, 
for  the  present  to  those  experiments,  which  relate  to  attraction  and 
repulsion,  and  the  passage  of  the  spark,  reserving  such  as  relate  to 
light  and  heat  to  future  sections.     The  following  effects  may  be  ob- 
served with  a  machine  of  moderate  powers,  the  rationale  of  which 
the  learner  will  readily  supply  from  the  propositions  given  in  Art.  378. 

(1.)  When  the  machine  is  turned,  a  downy  feather,  or  a  lock  of 
cotton  held  in  the  hand  by  a  conducting  thread,*  will  be  strongly  at- 
tracted towards  the  excited  surface. 

(2.)  A  skein  of  thread,  or  lock  of  fine  hair,  looped  and  suspend- 
ed by  the  loop  from  llie  prime  conductor,  will  exhibit  strong  repul- 
sions between  the  threads  or  hairs. 

(3.)  The  quadrant  electrometer  being  attached  to  the  prime  con- 
ductor, the  conducting  powers  of  different  substances  may  be  readily 
tried.  Thus,  an  iron  rod  held  in  the  hand,  and  applied  to  the  prime 

*  The  conducting  power  of  linen  or  cotton  threads  is  improved  by 
moistening  them  with  the  breath. 


204 


ELECTRICITY. 


conductor,  will  cause  the  index  of  the  electrometer  to  fall  instantly ; 
and  the  same  effect  will  follow  the  application  of  any  metallic  rod. 
A  wooden  rod  of  the  same  dimensions,  will  cause  the  index  to  de- 
scend more  slowly  ;  and  a  glass  rod  will  hardly  move  it  at  all.  These 
experiments  show  that  iron  is  ajperfect,  and  wood  an  imperfect  con- 
ductor,' and  glass  a  non-conductor.  In  the  same  manner  the  con- 
ducting powers  of  a  stick  of  sealing  wax,  a  roll  of  silk,  or  cloth,  and 
of  various  other  bodies,  may  be  illustrated. 

(4.)  If  a  pith  ball  or  feather  or  any  other  light  body  held  by  a 
silk  thread,  be,  presented  to  the  prime  conductor,  it  will  6rst  be  at- 
tracted and  then  repelled,  and  it  cannot  again  be  brought  into  con- 
tact with  the  electrified  conductor,  until  its  electricity  is  discharged 
by  communicating  with  the  finger  or  some  unelectrified  conductor. 

(5.)  By  placing  light  bodies  between  an  electrified  conductor  and 
an  uninsulated  body,  they  may  be  made  to  move  with  great  rapidity 
backwards  and  forwards,  from  one  surface  to  the  other,  being  alter- 
nately attracted  and  repelled  by  the  electrified  surface.  By  this 
means  are  performed  electrical  dances,  the  ringing  of  bells,  and  a 
variety  of  interesting  and  amusing  experiments. 

(6.)  If  the  rubber  be  insulated  while  the  machine  is  turned,  the 
rubber  and  the  glass  cylinder,  or  plate  will  be  found  to  be  in  differ- 
ent electrical  states ;  an  insulated  body  attracted  by  the  one  will  be 
repelled  by  the  other. 

Bodies  are  electrified  positively  by  connecting  them  with  the  glass, 
by  means  of  the  prime  conductor,  and  negatively  by  connecting  them 
with  the  rubber,  the  latter  being  insulated,  and  the  prime  conductor 
uninsulated. 

(7.)  An  electrified  body  frequently  exhibits  a  tendency  to  separate 
into  minute  parts,  these  parts  being  endued  with  the  power  of  mutual 
repulsion.  Thus,  a  lock  of  cotton,  when  electrified,  is  separated 
into  its  minutest  fibres.  Melted  sealing  wa^  when  attached  by  a 
wire  to  the  prime  conductor,  is  divided  into  filaments  so  small  as  to 
resemble  red  wool.  Water  dropping  from  a  capillary  syphon  tube, 
on  being  electrified,  is  made  to  run  out  in  a  great  number  of  exceed- 
ingly fine 'streams.  Water  spouting  from  an  air  fountain  (Art.  291.) 
is,  divided  into  a  number  of  rays,  presenting  the  appearance  of  a  brush.* 

(8.)  A  portion  of  electrified  air,  in  consequence  of  the  mutual  re- 
pulsion between  its  particles,  expands,  and  when  at  liberty  to  escape, 


LEYDEN    JAR. 


205 


becomes  rarefied.  Thus,  a  current  of  air  may  be  set  in  motion  from 
an  electrified  point,  or  small  ball,  or  be  made  to  issue  from  the  neck 
of  a  bottle. 

Such  are  some  of  the  leading  experiments  which  may  be  perform- 
ed with  the  common  electrical  machines,  in  addition  to  those  which 
are  connected  with  light  and  heat,  to  be  more  particularly  described 
hereafter. 

386.  The  force  of  electrical  attraction  or  repulsion^  at  different 
distances  from  an  electrified  body,  varies  inversely  as  the  square  of 

the  distance. 

\ 

Hence  electrified  bodies  exhibit  strong  attractions  and  repulsions 
only  when  very  near  to  each  other,  and  the  force  decreases  rapidly 
with  the  distance,  being  diminished  four  times  by  doubling  the  dis- 
tance, and  nine  times  by  trebling  it.  It  is  worthy  of  remark  that  the 
foregoing  law  is  the  same  as  that  of  gravitation. 

Electricity  resides  only  at  or  near  the  surfaces  of  bodies.  A  hol- 
low metallic  globe,  for  example,  takes  the  same  charge  as  a  solid 
globe  of  the  same  dimensions.  Bodies  of  different  figures,  however, 
have  the  electricity  distributed  over  their  surfaces  in  different  man- 
ners. Thus,  in  a  conductor  of  an  elongated  figure,  the  electricity 
is  accumulated  towards  the  two  ends,  and  more  or  less  withdrawn 
from  the  central  parts. 

The  Leyden  Jar. 

387.  This  instrument,  which  is  a  very  important  and  interesting 
article  of  electrical  apparatus,  consists  of  a  glass  jar,  coated  on  both 
sides  with  tin  foil,   except  a  space  on  the  upper  end, 

within  two  or  three  inches  of  the  top,  which  is  either 
left  bare,  or  is  covered  with  a  coating  of  varnish,  or  a 
thin  layer  of  sealing  wax.  To  the  mouth  of  the  jar  is 
fitted  a  cover  of  hard  baked  wood,  through  the  cen- 
ter of  which  passes  a  perpendicular  wire,  terminating 
above  in  a  knob,  and  below  in  a  fine  chain,  that  rests 
upon  the  bottom  of  the  jar.  On  presenting  the  knob 
of  the  jar  near  to  the  prime  conductor  of  an  electrical 
machine,  while  the  latter  is  in  operation,  a  series  of  sparks  passes 
between  the  conductor  and  the  Jar,  which  will  gradually  grow  more 


206  ELECTRICITY. 

and  more  feeble,  until  they  will  cease  altogether.  The  Jar  is  then 
said  to  be  charged.  If  now  we  take  the  Discharging  Rod,  (which 
is  a  crooked  wire,  armed  at  each  end  with  knobs, 
and  insulated  by  a  glass  handle,  as  in  Fig.  83,)  and 
apply  one  of  the  knobs  to  the  outer  coating  of  the 
Jar,  and  bring  the  other  to  the  knob  of  the  Jar,  a 
flash  of  intense  brightness,  accompanied  by  a  loud 
report,  immediately  ensues.  On  applying  the  dis- 
charging rod  a  second  time,  a  feeble  spark  passes, 
being  the  residuary  charge,  after  which  all  signs  of 
electricity  disappear,  and  the  Jar  is  said  to  be  discharged. 

388.  If,  instead  of  the  discharging  rod,  we  apply  one  hand  to  the 
outside  of  the  charged  Jar,  and  bring  a  knuckle  of  the  other  hand 
to  the  knob  of  the  Jar,  a  sudden  and  surprising  shock  is  felt,  con- 
vulsing the  arms,   and,  when  sufficiently  powerful,  passing  through 
the  breast. 

389.  The  Leyden  Jar  derives  its  name  from  the  place  of  its  dis- 
covery.    In  the  year  1746,  while  some  philosophers  of  Leyden 
were  performing  electrical  experiments,  one  of  them  happened  to 
hold  in  one  hand  a  tumbler  partly  filled   with  water,   to  a  wire  con- 
nected with  the  prime  conductor  of  an  electrical  machine.     When 
the  water  was  supposed  to  be  sufficiently  electrified,  he  attempted, 
with  the  other  hand,  to  detach  the  wire  from  the  machine  ;  but  as 
soon  as  he  touched  it,  he  received  the  electric  shock.     It  was  by 
imitating  this  arrangement,  that  the  Leyden  Jar  was  constructed  ; 
for  here  was  a  glass  cylinder,  having  good  conductors  on  both  sides, 
viz.  the  hand  on  the  outside,  and  the  water  on  the  inside,  which  were 
prevented  from  communicating  with  each  other  by  the  non-conduct- 
ing powers  of  the  glass.     A  metallic  coating,  as  tin  foil  or  sheet  lead, 
was  substituted  for  the  two  conductors,  and  a  jar  for  the  glass  cylin- 
der, and  thus  the  electrical  jar  was  constructed. 

390,-  Those  who  first  received  the  electric  shock  from  the  Leyden 
Jar,  gave  the  most  extravagant  accounts  of  its  effects.  M.  Musch- 
enbroeck,  a  philosopher  of  Leyden,  of  much  eminence,  said  that 
"  he  felt  himself  struck  in  his  arms,  shoulders  and  breast,  so  that  he 
lost  his  breath ;  and  it  was  two  days  before  he  recovered  from  the 


LEYDEN    JAR.  207 

effects  of  the  blow  and  the  terror ;  adding,  that  he  would  not  take  a 
second  shock  for  the  kingdom  of  France."  M.  Winkler,  of  Leipsic, 
testified,  that  "  the  first  time  he  tried  the  Leyden  experiment,  he  found 
great  convulsions  by  it  in  his  body;  and  that  it  put  his  blood  into  great 
agitation,  so  that  he  was  afraid  of  an  ardent  fever,  and  was  obliged 
to  use  refrigerating  medicines.  He  also  felt  a  heaviness  in  his  head, 
as  if  a  stone  lay  upon  it,  and  twice  it  gave  him  a  bleeding  at  the  nose.n 

391.  In  an  age  less  enlightened  than  the  present,  and  less  familiar 
with  the  wonders  of  philosophy  and  chemistry,  the  striking  and  truly 
surprising  effects  of  Electricity,  as  exhibited  by  the  Leyden  Jar,  would 
naturally  excite  great  admiration  and  astonishment.     Accordingly, 
showmen  travelled  with  this  apparatus  through  the  principal  cities  of 
Europe,  and  probably  no  object  of  philosophical  curiosity  ever  drew 
together  greater  crowds  of  spectators.    It  was  this  astonishing  experi- 
ment, (says  Dr.  Priestley,)  that  gave  eclat  to  Electricity.     From  this 
time,  it  became  the  subject  of  general  conversation.    Every  body  was 
eager  to  see,  and,  notwithstanding  the  terrible  account  that  was  re- 
ported of  it,  to  feel  the  experiment;  and  in  the  same  year  in  which 
it  was  discovered,  numbers  of  persons,  in  almost  every  country  in 
Europe,  got  a  livelihood  by  going  about  and  showing  it.     All  the 
electricians  of  Europe,  also,  were  immediately  employed  in  repeat- 
ing this  great  experiment,   and  in  attending  to  the  circumstances  of 
it.     With  similar  assiduity  and  unequalled  success,  Dr.  Franklin  be- 
took himself  to  experiments  on  the  Leyden  Jar.     He  effectually  in- 
vestigated all  its  properties,  by  very  diversified  and  ingenious  experi- 
ments, and  gave  the  first  rational  explanation  of  the  cause  of  its  phe- 
nomena.    The  following  experiments  may  be  easily  repeated. 

392.  (1.)  The  Jar  is  charged  by  bringing  the  knob  near  the  prime 
conductor,  while  the,  machine  is  in  operation.     One  mode  of  charg- 
ing the  Jar  has  been  already  mentioned  in  Art.  387.     It  may,  now- 
ever,  either  be  held  in  the  hand,  or  placed  on  the  table,  or  on  any 
conducting  support :  the  only  circumstance  to  be  attended  to  is,  that 
the  outside  shall  be  uninsulated.     A  Jar,  while  charging,  will  some- 
times discharge  itself  spontaneously.     This  effect  will  be  more  likely 
to  happen,  if  the  uncoated  interval  is  very  clean  and  dry,  and  may  be 
prevented  altogether,  by  previously  breathing  on  the  uncoated  part. 


208  ELECTRICITY. 

(2.)  The  opposite  sides  of  a  charged  Jar,  are  in  different  electrical 
states,  the  one  positive  and  the  other  negative.  Thus,  if  a  pith  ball, 
suspended  by  a  silk  thread,  be  applied  to  the  knobj  it  will  first  be  at- 
tracted to  it.  and  then  repelled ;  but  it  will  now  be  attracted  by  the 
outside  coating,  until  it  becomes  electrified  in  the  same  way,  and 
then  repelled,  and  so  on. 

(3.)  In  order  to  receive  the  charge,  the  outside  of  the  Jar  must  be 
uninsulated.  If  we  attach  a  string  to  the  knob  of  the  Jar,  and  sus- 
pend it,  in  the  air,  to  the  prime  conductor,  and  put  the  machine  in 
operation,  no  charge  will  be  communicated  to  the  Jar.  The  same 
result  will  follow,  if  the  Jar  stands  on  an  insulating  stand,*  or  is  in- 
sulated by  any  other  method.  An  insulated  Jar,  however,  may  be 
charged  by  connecting  its  knob  with  the  positive  conductor,  and  its 
outer  coating  with  the  rubber. 

(4.)  A  second  Jar  may  be  charged,  by  communication  with  the 
outside  of  the  first,  while  the  latter  is  receiving  its  charge.  The 
charge  communicated  to  the  second  Jar,  is  of  the  same  kind  as  that 
of  the  first,  and  nearly  of  the  same  degree  of  intensity,  provided  the 
capacity  of  the  two  Jars  be  the  same.  Moreover,  if  a  third,  a  fourth, 
or  any  number  of  Jars,  of  the  same  size,  be  connected,  in  a  similar 
manner,  with  each  other ;  namely,  having  the  knob  of  each  in  com- 
munication with  the  outside  coating  of  the  next  preceding, — then  all 
the  Jars  will  be  charged  with  the  same  kind  of  electricity,  but  the 
degree  of  intensity  will  decline  a  little  in  the  successive  Jars.  If 
the  charge  be  derived,  through  the  prime  conductor,  from  the  cylin- 
der or  plate,  as  is  usually  the  case,  it  will  be  the  positive  or  vitreous 
electricity. 

(5.)  JL  Jar  may  be  charged  negatively,  by  receiving  the  electricity 
of  the  rubber, — the  rubber  being  insulated,  and  the  prime  conductor 
uninsulated.  For  this  purpose,  the  chain  usually  attached  to  the 
rubber  may  be  transferred  to  the  prime  conductor. 

*  An  insulating  stand,   is  any  flat  support,  insulated  by  a  pillar  of 
glass.  *'*The  pillar  is  usually  a  solid  cylinder  of  glass,  from  six  to 
twelve  inches  long,  varnished  so  as  to  protect  it  from  moisture.     A 
junk  bottle,  surmounted  by  a  circular  piece  of  wood,  dry  and  varnish 
ed,  makes  a  very  good  insulating  support. 


LEYDEN    JAR.  209 

(6.)  When  two  Jars  are  charged^  the  one  positively  and  the  other 
negatively,  on  forming  a  communication  between  the  insides  of  both, 
by  connecting  the  two  knobs,  no  discharge  will  take  place,  unless  the 
outsides  be  in  conducting  communication.  Thus,  if  two  Jars  be 
charged,  the  one  from  the  prime  conductor  and  the  other  from  the 
rubber,*  and  placed  at  the  distance  of  a  few  inches  from  each  oth- 
er, on  insulated  supports,  on  connecting  the  two  knobs  by  the  dis- 
charging rod,  no  discharge  will  follow ;  but,  let  a  wire  be  laid  across 
the  supports,  touching  the  outside  of  each  Jar ;  then,  on  applying 
the  discharging  rod  to  the  two  knobs,  an  explosion  will  immediately 

>   ^ 

By  means  of  two  Jars  differently  charged,  and  placed  as  above, 
with  their  outsides  in  conducting  communication,  the  experiment .,/ 
may  be  exhibited,  which  is  called  the  Electrical  Spider.  It  consists 
of  a  small  piece  of  cork,  so  fashioned  as  to  represent  the  body  of  a 
spider,  and  blackened  with  ink,  having  a  number  of  black  linen 
threads  drawn  through  it  to  represent  the  legs.  This  is  suspended 
by  a  silk  thread,  half  way  between  the  knobs  of  the  two  Jars,  and 
vibrates  for  a  long  time  from  one  knob  to  the  other,  until  both  Jars 
are  discharged.  The  rationale  will  be  obvious  on  a  little  reflection. 

(7.)  The  charge  of  any  Jar  may  be  divided  into  definite  parts;  that 
is,  the  half,  the  fourth,  or  any  aliquot  part  of  the  charge  may  be  ta- 
ken. This  may  be  done  by  connecting  the  inner  and  outer  coating 
of  the  charged  jar,  with  the  inner  and  outer  coating  of  an  unelectrified 
jar,  of  the  same  size  and  thickness.  The  respective  charges  will  be 
measured  by  the  quadrant  electrometer,  (Fig.  80.) 

(8.)  The  electricity  is  accumulated  on  the  surface  of  the  glass,  and 
the  coatings  serve  merely  as  conductors  of  the  charge.  This  is  proved 
by  the  fact,  that  when  the  coatings  are  movable,  so  that  they  can  be 
taken  off  from  the  jar  after  it  is  charged,  neither  of  them  exhibits  the 
least  sign  of  electricity ;  while  if  another  pair  of  cqatings  is  substitu- 
ted, which  have  not  been  electrified,  on  forming  the  communication 
between  the  inside  and  outside,  the  usual  discharge  takes  place, 


*  And  both  may  be  thus  charged  at  the  same  time,  by  connecting 
one  with  the  insulated  rubber,  and  the  other  with  the  Insulated  prime 
conductor,  the  Jars  themselves  being  uninsulated. 

27 


210  ELECTRICITY. 

showing  that  the  whole  of  the  charge  was  retained  on  the  glass  sur- 
faces of  the  jar. 

(9.)  The  charge  of  a  Leyden  Jar  may  be  retained  for  a  long  time. 
If  the  surfaces  are  well  separated  from  each  other,  the  charge  re- 
mains for  many  days  or  even  weeks.  The  charge  is  usually  dissipa- 
ted by  the  motion  of  particles  of  dust,  or  other  conducting  substan- 
ces in  the  atmosphere,  from  one  of  the  coatings  to  the  other,  or  by 
the  uncoated  interval  becoming  'moist,  and  losing  its  insulating  power; 
consequently  a  jar  will  retain  its  charge  longer  in  dry  than  in  damp 
weather.  Covering  the  uncoated  part  of  the  jar  with  melted  seal- 
ing wax  or  varnish,  prevents  the  deposition  of  moisture  upon  it,  and 
consequently  tends  also  materially  to  prevent  the  dissipation  of  its 
charge. 

393.  For  the  purpose  of  making  the  theory  of  the  Leyden  Jar 
familiar,  we  may  now  recur  to  the  experiments  mentioned  in  Art. 
392,  and  attempt  the  explanation  of  them. 

In  the  structure  of  the  Jar,  we  recognise  the  operation  of  the  prin- 
ciple of  induction.  Here,  an  unelectrified  body  (the  outer  surface) 
is  brought  very  near  to  an  electrified  body,  (the  inner  surface,) 
without  the  possibility  of  communicating  with  each  other,  on  account 
of  the  non-conducting  properties  of  the  glass.  The  nearer  the  two 
surfaces  can  be  brought  to  each  other,  the  more  powerful  is  the  ef- 
fect of  induction,  that  effect  being  inversely  as  the  square  of  the  dis- 
tance. Accordingly,  the  thinner  the  jar,  the  more  powerful  is  the 
charge  it  will  receive;  but  the  danger  of  breaking  prevents  our  em- 
ploying such  as  are  very  thin. 

To  trace  the  process  of  charging  a  jar  a  little  more  minutely,  let 
us  suppose  the  jar  connected  with  the  prime  conductor  of  an  elec- 
trical machine,  from  which  a  spark  is  communicated  to  the  inner 
coating.  This,  according  to  the  principles  of  induction,  expels  a 
similar  quantity  of  the  same  fluid  from  the  opposite  unelectrified  sur- 
face, ana1  renders  that  negative,  in  the  same  degree  as  the  inside  is 
positive.  Being  negative,  it  increases  the  attraction  of  the  inner  sur- 
face fo£ the  opposite  species  of  fluid,  and  another  spark  is  received, 
which  again  expels  an  additional  quantity  of  the  same  species  of  fluid 
from  the  outside,  and  thus  the  two  surfaces  continue  to  act  upon  each 
other  reciprocally,  though- with  constantly  diminishing  power,  until 
the  ar  is  charged. 


ELECTRICAL    LIGHT.  211 

The  reason  also  is  plain,  why  the  outside  of  the  jar  must  be  un- 
insulated ;  since  it  is  only  in  such  case,  that  the  foregoing  process  of 
induction  can  take  place ;  and  we  readily  see  why  a  series  of  jars 
may  be  charged,  from  the  portion  of  electricity  which  is  expelled 
from  the  outside  of  the  first  jar. 

394.  When  a  jar  is  charged  negatively  from  the  rubber,  just  the 
opposite  process  in  all  respects  takes  place,  the  outside  becoming  posi- 
tive by  induction,   and  reacting  upon  the  inside.     The  case   men- 
tioned in  Art.  392,  (6.)   where  two  jars  differently  charged,   cannot 
be  discharged  except  their  outer  surfaces  be  in  conducting  commu- 
nication, will  be  readily  understood  ;  for  it  is  impossible  for  the  equi- 
librium to  be  restored  by  the  union  of  the  electricities  on  the  inside, 
while  the  outside  remains  electrified.     If  we  could  suppose  this  to 
take  place  for  a  moment,  and  the  electricity  within  to  be  restored  to 
its  natural  state,  it  wduld  again  be  immediately  decomposed  by  the 
inductive  influence  of  the  electrified  coating  without. 

395.  The  phenomena  of  the  Leyden  Jar,  may  be  equally  well 
explained,  by  substituting  the  terms  vitreous  and  resinous,  instead  of 
positive  and  negative,  on  the  supposition  of  two  fluids,  since  the  prin- 
ciples of  induction  apply  equally  well  to  both  hypotheses.     Thus,  it 
is  as  easy  to  suppose  that  the  resinous  electricity  is  induced  upon  the 
outside  by  the  attraction  of  the  vitreous  electricity  within,   as  it  is  to 
suppose  that  the  outside  becomes  negative  by  the  loss  of  a  portion  of 
its  natural  share ;  and  the  necessity  of  the  outer  surface  being  unfn- 
sulated,  is  as  apparent  in  the  one  case  as*  in  the  other.  * 


CHAPTER  III. 

OF  ELECTRICAL  LIGHT,  OF  THE  BATTERY,  AND  OF  THE  MECHAN- 
ICAL AND  CHEMICAL  AGENCIES  OF  ELECTRICITY. 

Electrical  Light. 

396.  Electrical  light  appears  whenever  the  fluid  is  discharged,  in 
considerable  quantity,  through  a  resisting  medium. 

Accordingly,  no  light  is  perceived  when  electricity  flows  freely 
through  good  conductors ;  but  if  such  conductors  suffer  any  interrup- 


212 


ELECTRICITY. 


tion,  as  by  the  intervention  of  a  space  of  air,  or  even  of  an  imperfect 
conductor,  then  the  attendant  light  becomes  manifest.  We  shall 
best  learn  the  properties  of  the  electrical  spark,  by  attending  to  a 
variety  of  experiments  in  which  it  is  exhibited.* 

A  glass  tube  rubbed  with  black  silk,  which  has  been  smeared  with 
a  little  electrical  amalgam,  will  yield  copious  sparks  and  flashes  of 
light.  The  tube  should  be  warm,  dry,  and  smooth,  and  of  a  size  not 
jess  than  two  feet  in  length,  and  three  fourths  of  an  inch  in  diameter. 

The  electrical  machine,  when  in  vigorous  action,  affords  bril- 
liant circles  and  streams  of  light.  In  order  to  render  the  light  af- 
forded by  turning  the  machine  abundant,  several  practical  expedients 
are  necessary.  All  parts  of  the  machine  must  be  dry  and  warm,  (but 
not  hot.)  It  is  useful  to  rub  very  freely  the  glass  plate  or  cylinder, 
with  an  old  silk  handkerchief.  Black  spots  or  lines  that  collect  on 
the  glass,  especially  when  the  amalgam  is  new,  are  to  be  carefully 
rubbed  off,  and  should  dust  or  down  collect  on  the  amalgam  of  the 
rubber,  this  must  be  removed.  The  action  of  the  cylinder  will  be 
increased  by  the  following  process :  smear  the  bottom  of  the  cylinder 
with  a  thin  coat  of  tallow ;  then  turn  the  machine  until  the  tallow  is 
all  taken  up  by  the  rubber  and  flap.  The  pores  of  the  flap  will  then 
become  rilled  with  tallow,  it  will  apply  itself  more  closely  to  the  cyl- 
inder, and  the  supply  of  electricity  will  become  more  copious.  A 
convenient  method  of  recruiting  the  action  of  the  machine,  is  to  coat 
a  circular  disk  of  paste  board  or  leather  with  amalgam,  and  to  apply 
it  to  the  glass  plate  or  cylinder  while  the  machme%is  turning. 

If  the  chain  be  removed  from  the  rubber  to  the  prime  conductor, 
so  that  the  former  shall  be  insulated  and  the  latter  uninsulated,  on 
bringing  the  ends  of  the  fingers  near  the  rubber,  a  stream  of  diluted 
Jight  will  pass  between  the  fingers  and  the  rubber. 

397.  The  electric  spark  passes,  with  increased  facility,  through 
rarefied  air  ;  and  the  distance  to  which  it  will  pass  between  two  con- 
ductors, is  augmented  as  the  rarefaction  is  made  more  complete. 

Instead  of  the  distance  of  five  or  six  inches,  which  is  the  limit  of 
the  sparfc  from  the  prime  conductor  of  an  ordinary  machine  in  the 


*  In  experiments  on  electrical  light,   the  room  is  supposed  to  br* 
dark.     They  appear  to  best  advantage  in  the  night. 


ELECTRICAL    LIGHT.  213 

open  air,  the  spark  will  pass  through  the  space  of  eighteen  inches  or 
more,  in  an  exhausted  receiver.  If  a  pointed  wire,  terminating  in  a 
knob  above,  be  introduced  into  the  top  of  a  tall  receiver,  and  the  re- 
ceiver be  placed  on  the  plate  of  the  air  pump,  on  connecting  the  knob 
of  the  wire  with  the  prime  conductor,  and  turning  the  machine,  a 
brush  of  light  only  will  appear  at  the  extremity  of  the  wire ;  but,  on 
exhausting  the  air,  this  brush  will  enlarge,  varying  its  appearance  and 
becoming  more  diffused  as  the  air  becomes  more  rarefied,  until  at 
length  the  whole  receiver  is  pervaded  by  a  beautiful  bluish  light, 
changing  its  color  with  the  intensity  of  the  transmitted  electricity,  and 
producing  an  effect  which  with  an  air  pump  of  considerable  power, 
is  pleasing  in  the  highest  degree. 

When  a  charged  jar  is  placed  under  the  receiver  of  an  air  pump, 
as  the  exhaustion  proceeds,  a  luminous  current  flows  over  the  edge  of 
the  jar  from  the  positive  to  the  negative  side,  until  the  equilibrium  is 
restored.  Electric  light  exhibits  a  very  beautiful  appearance,  as  it 
passes  or  flows,  through  the  Torricellian  Vacuum.*  The  color 
is  of  a  very  delicate  bluish  or  purple  tinge,  and  the  light  per- 
vades the  entire  space.  But  the  most  pleasing  exhibtions  of  this 
kind,  are  made  by  forming  an  artificial  atmosphere  of  vapor  in  the 
Torricellian  tube.  Ether  or  alcohol,  passes  into  the  state  of  vapor 
when  the  pressure  of  the  atmosphere  is  removed ;  and  accordingly, 
on  introducing  a  drop  of  one  of  these  fluids  into  the  Torricellian  va- 
cuum, it  immediately  evaporates  and  fills  the  void.  If,  now,  a  strong 
spark  be  passed  from  the  prime  conductor  through  this  vapor,  the 
spark  will  exhibit  various  colors  :  in  ether,  it  is  an  emerald  green,  or 
mingled  red  and  green  ;  in  alcohol  it  is  red  or  blue ;  but  the  colors 
vary  somewhat  with  the  distances  at  which  they  are  seen. 

398.  In  condensed  air,  on  the  contrary,  the  spai'k  passes  with 
greater  difficulty  than  ordinary.  In  such  case,  also,  its  whiteness, 
and  brilliancy  are  augmented,  and  its. course  is  zigzag.  These  ap- 
pearances are  even  exhibited  by  passing  the  spark  through  confined 
air,  of  only  the  ordinary  density.  The  colors  of  the  spark,  are 
pleasingly  varied  by  passing  it,  in  a  condensed  form,  as  in  the  Ley- 

• 

*  This  is  the  vacuum  produced  by  means  of  quicksilver  in  an  in- 
verted  glass  tube,  as  the  barometer,  Art.  295. 


214  ELECTRICITY. 

den  Jar,  through  media  of  different  kinds.  The  experiment  is  per- 
formed by  making  the  given  body  form  a  part  of  the  circuit  of  com- 
munication, between  the  inside  and  outside  of  the  Leyden  Jar.  A 
ball  of  ivory  in  this  situation  exhibits  a  beautiful  crimson ;  an  egg.  a 
similar  color-  but  somewhat  lighter ;  a  lump  of  sugar,  gives  a  very 
white  light,  which  remains  for  some  time  after  the  spark  has  passed  ; 
and  fluor  spar  exhibits  an  emerald  green  light,  or,  in  some  cases,  a 
purple  light,  which  also  continues  to  glow  in  the  dark  for  some 
seconds.  The  great  intensity  of  the  light  is  shown  by  the  strong 
illumination  which  the  sparks  in  the  jar  communicate  to  bodies  slightly 
transparent.  Thus  an  egg  has  its  transparency  greatly  increased ; 
and  if  the  thumb  be  placed  over  the  space  which  separates  the  two 
conducting  wires  that  communicate  with  the  two  sides  of  the  jar  re- 
spectively, the  illumination  is  so  powerful,  that  the  blood  vessels  and 
interior  organization  of  the  organ  may  be  distinctly  seen. 

399.  Metallic  conductors,  if  of  sufficient  size,  transmit  electricity 
without  any  luminous  appearance,  provided  they  are  perfectly  con- 
tinuous 5  but  if  they  are  separated  in  the  slightest  degree,  a  spark 
will  occur  at  every  separation.     On  this  principle,  various  devices 
are  formed  by  pasting  a  narrow  band  of  tin  foil  on  glass,  in  the  re- 
quired form,  and  cutting  it  across  with  a  pen  knife,  where  we  wish 
sparks  to  appear.     If   an  interrupted  conductor  of  this  kind  be 
pasted  round   a  glass  tube  in  a  spiral  direction,  and  one  end  of  the 
tube  be  held  in  the  hand,  and  the  other  be  presented  to  an  electrified 
conductor,  a  brilliant  line  of  light  surrounds  the  tube,  which  has  been 
called  the  spiral  tube,  or  diamond  necklace.     By  enclosing  the  spiral 
tube,  in  a  larger  cylinder  of  colored  glass,  the  sapphire,  topaz,  eme- 
rald and  other  gems  may  be  imitated.     Words,  flowers,  and  other 
complicated  forms,  are  also  exhibited  nearly  in  the  same  manner,  by 
a  proper  disposition  of  an  interrupted  line  of  metal,  on  a  flat  piece 
of  glass. 

400.  The  light  of  the  electric  spark,  is  not  a  Constituent  part  of 
electricity,  but  arises  from  the  sudden  compression  of  the  air,  or  other 
mediumFthrough  which  it  passes. 

It  is  well  known,  that  air  is  capable  of  affording  a  spark  by  sudden 
compression.     There  is  a  kind  of  match  constructed  on  this  princi- 


ELECTRICAL    LIGHT. 


215 


Fig.  84. 


pie,  in  which  a  small  portion  of  air  contained  in  a  close  cylinder,  be- 
ing suddenly  compressed  by  forcing  down  a  piston,  yields  a  spark 
sufficient  to  light  a  quantity  of  tinder  at  the  bottom  of  the  cylinder. 
Now  it  is  found  by  actual  experiment,  that  electricity  has  the  power 
of  condensing  air.  This  fact  is  shown  by  means  of  a  small  instrument 
called  Kinnersley's  Air  Thermometer.  It  consists  of 
a  glass  tube,  closed  air  tight  at  the  two  ends  by  brass 
caps,  through  each  of  which  passes  a  movable  wire, 
terminated  within  by  a  small  ball.  Through  the  low- 
er cap  is  inserted  a  small  glass  tube  open  at  both  ex- 
tremities, and  turned  upwards  parallel  to  the  cylin- 
der. Into  this  tube  is  introduced  a  quantity  of  water 
sufficient  to  cover  the  bottom  of  the  cylinder,  and  of 
course  to  rise  a  little  way  into  the  tube.  The  two 
balls  being  set  at  some  distance  from  each  other,  and 
a  spark  from  the  Leyden  Jar  being  passed  between 
them,  the  air  within  is  suddenly  rarefied,  and  the  wa- 
ter ascends  in  the  tube,  and  again  descends,  when  the 
explosion  is  over.  This  sudden  rarefaction  of  a  portion 
of  air  before  the  electric  spark,  must  cause  a  sudden  and  powerful 
compression  in  the  portions  of  air  immediately  adjacent.  The  im- 
mense velocity  of  the  spark  must  greatly  increase  the  resistance, 
and  of  course  the  force  of  compression.  This  appears  to  be  an  ad- 
equate cause  for  the  production  of  the  light  that  accompanies  the 
electric  discharge,  and  hence  we  conclude,  that  light  is  not  inherent 
in  the  fluid  itself.  The  greater  density  and  brilliancy  of  the  spark 
in  condensed  air,  and  its  feebleness  and  difFuseness  in  a  rarefied  me- 
dium, are  facts  which  accord  well  with  the  supposed  origin ;  and  the 
zigzag  form  of  the  spark  when  long,  or  when  passing  through  con- 
densed air  is  well  explained  ,by  the  same  theory.  For  the  electric 
fluid  in  its  passage  through  the  air,  condenses  the  air  before  it,  and 
thus  meet  with  a  resistance  which  turns  it  off  laterally;  in  this  direc- 
tion it  is  again  condensed,  and  has  its  course  again  changed;  and  so 
on,  until  it  reaches  the  conductor  towards  which  it  is  aiming.  The 
zigzag  form  of  lightning  is  accounted  for  on  this  principle. 

Electrical  light  is  found  by  optical  experiments,  to  have  precisely 
the  same  nature  with  the  light  of  the  sun,  being  like  this  resolved  into 
various  colors  by  the  prism,  and  possessing  other  properties,  to  be 
described  under  the  head  of  Optics,  which  identify  it  with  solar  light. 


216  ELECTRICITY. 

Battery. 

401.  Jin  electric  battery  consists  of  a  number  of  Ley  den  Jars  so 
combined)  that  the  whole  may  be  either  charged  or  discharged  at  once. 

Very  large  jars  cannot  be  obtained  ;  it  is  rare  to  find  one  more 
than  two  feet  high,  by  one  and  a  half  in  diameter.  Yet  some  of 
the  mechanical  effects  of  electricity,  to  be  described  hereafter,  re- 
quire a  much  greater  accumulation  of  the  fluid  than  can  be  obtained 
from  any  single  jar.  t  The  battery  is  constructed  as  follows.  Large 
jars,  twelve  or  fourteen  inches  high,  by  five  or  six  inches  in  diameter 
are  coated  like  ordinary  Leyden  Jars.  Twelve  of  these  constitute  a 
battery  sufficiently  powerful  for  most  purposes,  but  the  power  of  the 
battery  may  be  carried  to  an  indefinite  extent  by  increasing  the  num- 
ber of  jars.  When  the  number  is  twelve,  they  are  placed  four  in 
a  row  in  a  box,  the  bottom  of  which  is  coated  with  tin-foil,  by  means 
of  which  the  outsides  of  the  jars  are  all  in  conducting  communica- 
tion. Each  jar  is  separated  from  the  rest  by  a  slight  partition  of 
wood.  To  connect  the  insides  of  the  jars,  their  knobs  are  joined 
by  large  brass  wires.  It  is  obvious,  therefore,  that  the  battery 'is 
equivalent  to  a  single  jar  of  enormous  size,  comprehending  the  same 
number  of  square  feet. 

The  object  of  the  battery  is  to  accumulate  a  great  quantity  of  the 
electric  fluid,  which  is  in  proportion  to  the  extent  of  surface  ;  the  in- 
tensity, or  elastic  force,  as  indicated  by  the  quadrant  electrometer, 
is  no  greater  in  the  battery  when  charged,  than  in  a  single  charged 
jar.  The  battery,  like  the  common  jar,  is  charged  by  bringing  the 
inside  into  communication  with  the  prime  conductor  of  an  active  and 
powerful  electrical  machine  :  it  is  discharged,  as  usual,  by  forming 
a  connexion  between  the  inside  and  outside,  commonly  by  means  of 
the  discharging  rod. 

402.  The  largest  machine  and  battery  hitherto  constructed,  were 
made  for  the  Teylerian  m'useum,  at  Haarlem.  It  consists  of  two  cir- 
cular plates  of  glass  each  five  feet  five  inches  in  diameter.  The 
prime'eonductor  consists  of  several  pieces,  and  is  supported  by  three 
glass  pillars,  nearly  five  feet  in  length.  The  force  of  two  men  is  re- 
quired to  work  the  machine  ;  and  when  it  is  required  to  be  put  in  ac- 
tion for  any  length  of  time,  four  are  necessary. 


EFFECTS    OF    ELECTRICITY.  217 

At  its  first  construction  nine  batteries  were  applied  to  it,  each  hav- 
ing fifteen  jars,  every  one  of  which  contained  a  square  foot  of  coat- 
ed glass  ;  so  that  the  grand  battery,  formed  by  the  combination  of  all 
these,  contained  one  hundred  and  thirty  five  feet.  As  examples  of 
the  great  power  of  the  Teylerian  machine,  we  may  mention  the 
following ;  it  charged  a  Leyden  jar  by  turning  the  handle  half  round, 
— a  charge  which  the  jar  would  receive,  and  lose  by  discharging  it- 
self spontaneously,  eighty  times  in  a  minute.  A  single  spark  from 
the  conductor  melted  a  considerable  length  of.  gold  leaf.  A  spark, 
or  zigzag  stream  of  fire  would  dart  from  the  prime  conductor  to  a 
neighboring  conductor  to  the  distance  of  ten  feet.  A  wire  three 
eighths  of  an  inch  in  diameter,  was  found  to  be  insufficient  to  trans- 
mit the  whole  charge  of  the  prime  conductor,  but  the  wire  would  give 
small  sparks  to  a  conductor  brought  near  to  it.  The  sphere  of  influ- 
ence (Art.  379.)  extended  to  the  distance  of  forty  feet,  so  as  sensibly 
to  affect  the  pith  ball  electrometer.  The  spider  web  sensation  (or 
that  peculiar  sensation  resembling  that  of  the  spider's  web)  which  is 
experienced  by  holding  an  excited  glass  tube  to  the  face,  was  felt  by 
bystanders  to  the  distance  of  eight  feet  from  the  machine. 

Mechanical  Effects  of  Electricity. 

403.  The  sound  produced  by  an  electric  discharge,  is  ascribed  to 
the  sudden  collapse  of  the  air,  which  has  been  displaced  by  the  passage 
of  the  electric  fluid. 

Hence  the  sound  is  greater  in  proportion  to  the  quantity  and  inten- 
sity of  the  charge.  A  battery,  when  fully  charged,  gives  a  loud  ex- 
plosion. 

404.  Imperfectly  conducting  substances,  through  which  a  powerful 
electric  charge  is  passed,  are  torn  asunder  with  more  or  less  violence. 

A  large  Leyden  Jar  is  sufficient  for  exhibiting  some  of  these  me- 
chanical effects :  others  require  the  power  of  the  Battery.  When 
the  charge  is  passed  through  a  thick  card,  or  the  cover  of  a  book,  a 
hole  is  torn  through  it,  which  presents  the  rough  appearance  of  a  bur 
on  each  side.  By  means  of  the  Battery,  a  quire  of  strong  paper 
may  be  perforated  in  the  same  manner ;  and  such  is  the  velocity  with 

28 


218  ELECTRICITY. 

which  the  fluid  moves,  that  if  the  paper  be  freely  suspended,  not 
the  least  motion  is  communicated  to  it.  (See  Art.  29,)  Pieces  of 
hard  wood,  of  loaf  sugar,  of  stones,  and  many  other  brittle  non-con- 
ductors, are  broken  or  even  torn  asunder  with  violence,  by  a  power-. 
ful  charge  from  the  battery.  If  two  wires  be  introduced  into  a  soft 
piece  of  pipe  clay,  and  a  strong  charge  be  passed  through  them,  the 
clay  will  be  curiously  expanded  in  the  interval  between  the  wires. 

The  expansion  of  fluids  by  electricity  is  very  remarkable,  and 
productive  of  some  singular  results.  When  the  charge  is  strong,  no 
glass  vessel  can  resist  the  sudden  impulse.  JBeccaria  inserted  a  drop 
of  water  between  two  wires,  in  the  center  of  a  solid  glass  ball  of  two 
inches  diameter  ;  on  passing  a  shock  through  the  drop  of  water,  the 
ball  was  dispersed  with  great  violence.  In  like  manner,  by  the  sud- 
den expansion  of  a  small  body  of  confined  air,  strongly  electrified, 
explosions  maybe  produced,  and  bodies  that  resist  its  expansion  are 
projected  with  violence.  Even  good  conductors,  when  minutely  di- 
vided, are  expanded  by  electricity.  Thus,  mercury,  confined  in  a 
capillary  glass  tube,  will  be  expanded  with  a  force  sufficient  to  splin- 
ter the  tube. 

Chemical  Effects  of  Electricity. 

405.  By  means  of  Electricity,  more  or  less  accumulated,  a.  variety 
of  chemical  effects  may  be  produced;  such  as  the  combustion  of  inflam- 
mable bodies,  the  oxidation,  fusion,  and  even  combustion  of  metals, 
the  separation  of  compounds  into  their  elements,  or  the  union  of  ele- 
ments into  compounds. 

Ether  and  alcohol  may  be  inflamed  by  passing  the  electric  spark 
through  them ;  nor  is  the  effect  diminished  by  communicating  the 
spark  by  means  of  a  piece  of  ice  or  any  othefr  cold  medium.  The 
finger  may  be  conveniently  employed  to  inflame  these  substances. 
Phosphorus,  resin,  and  other  solid  combustible  bodies,  may  be  set 
on  fire  by  the  same  means ;  gunpowder  and  the  fulminating  powders 
may  be  exploded  ;  and  a  candle  may  be  lighted.  Gold  leaf  and  fine 
iron  wire^may  be  burned,  by  a  charge  from  the  battery.*  Wires  of 
lead,  tin,  zinc,  iron,  copper,  platina,  silver  and  gold,  when  subjected 
to  the  charge  of  a  very  large  battery,  burn  with  explosion  and  are 
converted  into  oxides. 


MOTIONS  OF  THE  ELECTRIC  FLUID.  219 

The  same  agent,  moreover,  is  capable  of  reviving  these  oxides ; 
that  is,  restoring  them  to  the  state  of  pure  metals.  By  a  similar 
contrariety  of  properties,  water  is  decomposed  into  its  gaseous  ele- 
ments, and  the  same  elements  are  reunited  to  form  water ;  and  the 
constituent  gases  of  atmospheric  air  are,  by  passing  a  great  number 
of  electric  charges  through  a  confined  portion  of  air,  converted  into 
nitric  acid. 

Motions  of  the  Electric  Fluid. 

406.  The  velocity  of  the  electric  fluid  is  apparently  instantaneous. 
A  circuit  of  four  miles  has  been  formed,  by  means  of  wire,  between 
the  inside  and  outside  of  a  Leyden  Jar,   and  no  perceptible  interval 
was  occupied  during  the  discharge.     Analogy,  however,  would  lead 
us  to  believe  that  Electricity,  like  light,  is  progressive  in  its  motions, 
but  that  it  moves  with  a  velocity  too  great  to  be  measured,   except 
for  intervals  of  immense  extent.* 

407.  The  electric  fluid,  in  its  route,  selects  the  best  conductors. 
The  Leyden  Jar  may  be   discharged  with  a  wire  held  in  the  hand, 
without  the  insulating  handle  used  in  the  Discharging  Rod ;  since 
metallic  wire  is  a  better  conductor  than  the  hand,  and  the  fluid  will 
take  its  route  through  that  in  preference  to  the  hand.     But  if  a  wood- 
en discharger  be  substituted  for  the  wire,  the  shock  will  be  felt,  since 
animal  substances  are  better  conductors  than  wood.     It  is  necessary 
to  remark,  however,  that  when  the  charge  is  very  intense  or  the 
quantity  great,  as  in  the  Battery,  then  some  portion  of  the  fluid  will 
escape  from  the  discharging  wire  and  pass  through  the  hand.     In 
such'  cases,  therefore,  it  is  prudent  to  make  use  of  the  Discharging 

Rod. 

* 


*  The  velocity  of  light  appears  to  be  instantaneous,  for  such  dis- 
tances as  four  miles ;  but  when  such  intervals  are  taken  as  the  diame- 
ter of  the  earth's  orbit,  light  is  found  to  have  a  progressive  velocity 
of  192,500  miles  per  second^  If,  therefore,  electricity  actually  moves 
with  a  progressive  velocity  like  that  of  light,  still  the  time  occupied 
in  traversing  the  space  of  four  miles  would  be  inappreciable,  since  it 
would  equal  only  about  j  oT7¥  part  of  a  second. 


220  ELECTRICITY. 

Lightning,  in  striking  a  building,  usually  takes  a  course  which  indi- 
cates the  preference  of  the  fluid  for  the  best  conductors. 

408.  The  electric  fluid  will  sometimes  take  a  shorter  route  through 
a  worse  conductor,  in  preference  to  a  longer  route  through  a  better 
conductor.     The  spark  will  pass  through  a  short  space  of  air,  instead 
of  following  a  small  wire  thirty  or  forty  feet.     The  preference  of 
the  shorter  route  is  sometimes  indicated  in  taking  the  electric  shock. 
"While  one  person  is  receiving  the  shock  from  the  Leyden  Jar,   an- 
other may  grasp  his  arm  without  feeling  the  least  effect  from  the 
charge. 

409.  The  course  of  the  charge  is  frequently  determined  by  the 
influence  of  points^  either  in  dissipating  or  in  receiving  the  fluid. 
Sharp  points  connected  with  the  best  conductors,  greatly  favor  the 
dispersion  of  the  fluid   during  its  passage,   and  sharp  pointed  con- 
ductors draw  the  charge  towards  them,  from  a  great  distance  around. 
The  finest  needle,  held  in  the  hand  towards  the  knob  of  one  of  the 
jars  of  a  charged  battery,  will  silently  discharge  it,  in  a  few  seconds; 
and  if  we  apply  one  hand  to  the  outside  of  a  Leyden  Jar,  and  with 
the  other  bring  a  fine  needle  to  the  knob  of  the  Jar,  only  a  compara- 
tively feeble  shock  will  be  felt,  the  charge  being  rapidly  dissipated 
while  the  needle  is  approaching  the  knob. 


CHAPTER  IV. 

OF  THE  EFFECTS  OF  ELECTRICITY  UPON  ANIMALS,  AND  OF  THE 
LAWS  OF  ELECTRICAL  PHENOMENA.  . 

410.  We  have  already  several  times  incidentally  adverted  to  the 
shock  communicated  to  the  animal  system,  when  it  is  brought  into 
the  electric  circuit,  so  that  the  charge  passes  through  it.  We  now 
propose  to  consider  this  interesting  part  of  the  subject  more  particu- 
larly. 

The  Electric  Shock  is  received,  whenever  the  animal  system  is 
made  a  part  of  the  conducting  communication)  between  the  inside 
and  outside  of  a  charged  Leyden  Jar.  A  convenient  method  of  ad- 
ministering the  shock,  is  to  place  the  charged  jar  on  a  table,  resting 


EFFECTS    ON    ANIMALS.  221 

immediately  on  a  metallic  plate,*  as  a  plate  of  tin,  lead,  or  copper; 
then  grasping  a  metallic  rod  in  each  hand,  touch  one  of  them  to  the 
plate  and  the  other  to  the  knob  of  the  Jar,  and  a  sudden  convulsion 
of  the  limbs  or  the  breast  will  be  experienced,  more  or  less  violent 
according  to  the  strength  of  the  charge.  The  effect  is  greatly  height- 
ened by  feelings  of  dread  or  apprehension,  and  it  may  be  resisted  to 
a  considerable  degree  by  voluntary  effort.  A  slight  charge  affects 
only  the  fingers  or  the  wrists ;  a  stronger  charge  convulses  the  large 
muscles  above  the  arm-pits ;  a  still  greater  charge  passes  through 
the  breast  and  becomes  in  some  degree  painful.  Electricians,  how- 
ever, have  frequently  adventured  upon  charges  sufficiently  powerful 
to  convulse  the  whole  frame. 

411.  The  shock  may  be  communicated  to  any  number  of  persons 
at  once.     This  is  usually  effected  by  their  joining  hands,  while  the 
first  in  the  series  holds  one  of  the  metallic  rods,  with  which  he 
touches  the  plate  or  outside  of  the  jar,  and  the  last  in  the  series 
holds  the  other  rod,  with  which  he  touches  the  knob  of  the  Jar,  at 
which  instant  the  whole  number  receive  the  shock  at  the  same  mo- 
ment, and  that  however  extensive  the  circle  of  persons  may  be.    The 
charge  of  a  large  battery  is  sufficient  to  destroy  human  life,  especially 
if  it  be  received  through  the  head.     By  standing  on  the  Insulating 
Stool,  which  is  a  stool  with  glass  feet,  a  person  becomes  an  insulated 
conductor,  and  may  be  electrified  like  any  other  insulated  conductor. 
A  communication  being  made  with  the  machine,  the  fluid  pervades 
the  system,  but  excites  hardly  any  sensation  except  a  prickling  of 
the  hair,  which  at  the  same  time  rises  and  stands  erect ;  for  the 
hairs,  being  similarly  electrified,  mutually  repel  each  other. 

412.  While  in'this  situation,  the  human  system  exhibits  the  same 
phenomena  as  the  prime  conductor  when  charged ;  that  is,  it  attracts 
light  bodies,  gives  a  spark  to  conductors  brought  near  it,  and  commu- 
nicates a  slight  shock  to  another  person  who  receives  the  spark  from 
it.     Indeed,  the  same  shock  is  felt  by  both  parties. 

*  It  is  safer  to  employ  such  a  plate  than  to  bring  the  conducting  rod 
immediately  into  contact  with  the  outside  coating  of  the  Jar;  for,  in 
such  case,  persons  unaccustomed  to  receive  the  shock,  are  apt  to  over- 
turn the  Jar  and  break  it. 


222  ELECTRICITY. 

By  means  of  the  insulating  steol,  the  most  delicate  shocks  may  be 
given  ;  for  the  charge  may  be  drawn  off  from  any  part,  by  imperfect 
conductors.  Thus,  a  pointed  piece  of  wood  will  draw  off  the  charge 
from  the  eye,  in  a  manner  so  gentle,  as  to  secure  that  tender  organ 
against  any  possibility  of  injury.  By  a  variety  of  conductors,  of  dif- 
ferent powers,  and  by  points  and  balls,  the  sensations  may  be  accom- 
modated, with  much  delicacy,  to  the  state  of  the  patient,  or  to  the 
nature  of  the  affected  part. 

413.  The  shock  may  be  communicated  directly  to  any  individual 
part  of  the  system,  without  affecting  the  other  parts,  by  making  that 
part  form  a  portion  of  the  electric  circuit,  between  the  inside  and 
outside  of  a  Leyden  Jar.     Thus,  let  it  be  required  to  electrify  an 
arm.     Two  directors,  (consisting  of  wires  terminating  in  brass  knobs, 
and   insulated  by  glass  handles,)  are  connected  by  chains  with  the 
knob,   and  the  outside  coating  of  a  charged  Jar ;  then  on  applying 
one  of  the  directors  to  the  hand,  and  the  other  to  the  naked  shoulder, 
the  arm  is  convulsed.     In  cases  where  the  patient  requires  only  a 
moderate  shock,  the  charge  is  regulated  by  a  contrivance  attached 
to  the  Jar  called  Lane's  Discharging  Electro-  Fig.  85 
meter,  represented  in  Fig.  85.     S  is  a  stick  of 

solid  glass ;  B,  R,  two  brass  knobs,  connected 
by  a  wire,  which  slides  back  and  forth  in  such 
a  way  that  it  may  be  set  at  any  required  dis- 
tance from  the  knob  of  the  Jar.  If  the  ball  B 
be  set  in  contact  with  the  knob,  then  on  touch- 
ing the  ball  and  the  outer  coating  of  the  Jar; 
the  entire  charge  of  the  Jar  is  received ;  but 
by  removing  the  ball  B  from  the  knob,  the  half, 
fourth,  or  any  aliquot  part  of  the  charge,  may  be  taken  at  first,  and 
afterwards  the  remainder  may  be  taken  by  sliding  the  wire  nearer 
to  the  Jar. 

414.  Soon  after  the  discovery  of  the  Leyden  Jar,  commenced 
the  application  of  Electricity  to  Medicine;  and  Medical  Electricity, 
became  ^henceforth  a  distinct  branch  of  the  science.     The  first  cure 
said  to  have  been  effected  by  this  agent,  was  upon  a  paralytic. 
Electricity  shortly  became  very  celebrated  for  the  cure  of  this  dis- 
order, and  patients  flocked  in  great  numbers  to  the  practitioners  of 


CAUSE    OF    ELECTRICAL    PHENOMENA.  223 

this  branch  of  the  profession.  As  usual,  the  effects  of  this  new 
remedy  were  greatly  exaggerated,  and  it  was  widely  extolled,  not 
only  for  the  cure  of  palsy,  but  of  all  other  diseases.  It  was  even 
pretended  that  the  virtues  of  the  most  valuable  medicines  might  be 
transferred  into  the  system  through  the  medium  of  electricity,  pre- 
serving their  specific  properties  in  the  same  manner  as  when  taken  by 
way  of  the  stomach.  Preparations  of  this  kind  were  called  Medicated 
Tubes.  Pavati,  an  Italian,  and  Winkler,  a  German,  were  especially 
celebrated  for  this  species  of  practice.  The  mode  was  to  enclose 
the  medicines  in  a  glass  tube,  then  to  excite  the  tube,  and  with  it  to 
electrify  the  patient.  In  this  way,  it  was  said,  the  healing  virtues  of 
the  medicines  were  communicated  to  the  system  in  a  manner  at  once 
efficacious  and  agreeable. 

415.  Pretensions  so  extravagant  could  not  long  be  sustained,  and 
the  natural  consequence  was  that  the  use  of  electricity  in  medicine 
soon  fell  into  great  neglect,  and  has  remained  in  this  situation  to  the 
present  time.    There  are,  however,  certain  properties  inherent  in  this 
agent,  which  deserve  the  attention  of  the  enlightened  physician,  and 
inspire  the  hope  that,  in  judicious  hands,  it  may  still  be  auxiliary  to 
the  healing  art.     First,  the  great  activity  of  this  agent,  particular- 
ly the  facility  and  energy  with  which  it  can  be  made  to  act  upon  the 
nervous  system,  indicate  that  it  has  naturally  important  relations  to 
medicine.     The  power  of  being  applied,  locally,  to  any  part  of  the 
system,  renders  it  a  convenient  application  in  cases  where  other  local 
remedies  cannot  be   administered.     Secondly,    the   acknowledged 
property  of  electricity  to  promote  the  circulation  of  fluids  through 
capillary  tubes,  Art.  385.  (7.)  suggests   the  probability  of  its  being 
efficacious  in  promoting  the  circulation  of  the  fluids  of  the  animal  sys- 
tem, and  in  increasing  the  quantity  of  insensible  perspiration.  Thirdly, 
in  the  history  of  medical  electricity  are  recorded  well  attested  cures, 
effected  by  means  of  electricity,  of  such  diseases,  as  palsy,  rheumatism, 
gout,  indolent  tumors,  deafness,  and  A  variety  of  other  disorders. 

Cause  of  Electrical  Phenomena. 

416.  For  the  sake  of  convenience,  and  for  the  purpose  of  avoid- 
ing repetition  and  circumlocution,  we  have  made  occasional  use  of 
the  phrase  electric  fluid.     It  may  be  proper  now  to  inquire  whether 


224  .  ELECTRICITY. 

there  are  any  just  grounds  for  supposing  such  a  fluid  or  fluids  to  be 
present  in  electrical  phenomena. 

There  are  two  modes  by  which  the  existence  of  such  a  fluid  may 
be  rendered  probable  :  the  first  is,  by  showing  that  such  a  supposi- 
tion is  conformable  to  the  analogy  of  nature ;  the  second  is,  by  prov- 
ing that  the  agent  of  electrical  phenomena  exhibits  the  properties  of 
a  fluid. 

417.  First,  there  are  some  reasons  derived  from  analogy  for  believ- 
ing in  the  existence  of  an  electric  fluid.  (1.)  The  reasons  in  favor 
of  supposing  the  light  and  heat  are  caused  by  the  agency  of  peculiar 
fluids,  (arguments,  however,  that  we  cannot  discuss  here,)  which 
have  induced  a  general  belief,  are  for  the  most  part  equally  applicable 
to  electricity.  (2.)  In  the  present  state  of  our  knowledge,  the  most 
subtile  of  all  fluids,  indeed  the  most  attenuated  form  of  matter,  is  hy- 
drogen gas,  of  which  one  hundred  cubic  inches  weigh  only  two  and  a 
quarter  grains,  which  is  nearly  fourteen  times  lighter  than  common  air. 
But  at  no  distant  period,  means  had  not  been  devised  by  mankind  for 
proving  the  materiality  of  common  air,  nor  even  of  identifying  the 
existence  of  the  other  gases  which  now  bear  so  conspicuous  a  part 
in  experimental  philosophy.  But  as  knowledge  and  experimental 
researches  have  advanced,  a  series  of  fluids  still  more  subtile  than 
air,  have  come  to  light,  until  we  have  reached  a  body  nearly  fourteen 
times  lighter  than  air,  at  which,  at  present,  the  series  stops.  Is  it 
probable,  however,  that  nature  stops  in  her  processes  of  attenuation 
precisely  at  the  point  where,  for  want  of  more  delicate  instruments, 
or  more  refined  and  powerful  organs  of  sensation,  our  methods  of 
investigation,  and  powers  of  discrimination,  come  to  their  limit  ?  An 
examination  of  the  general  analogies  of  nature,  will  lead  us  to  think 
otherwise.  The  subordination  which  exists  among  the  different 
classes  of  bodies  that  compose  the  other  departments  of  nature,  is 
endless,  or  at  least  indefinite.  In  the  animal  creation,  for  example, 
beginning  with  the  mammoth  or  the  elephant,  we  descend  through 
numerous  tribes  to  the  insect  which  is  barely  visible  in  the  sunbeam. 
Before  Jjuman  ingenuity  had  devised  means  of  aiding  the  powers  of 
vision,  the  naturalist  might  have  fixed  this  as  the  limit  of  the  animal 
creation.  But  the  invention  of  the  microscope  has  carried  the  range 
of  human  vision  immeasurably  farther;  and  at  each  successive  im- 


CAUSE    OF    ELECTRICAL    PHENOMENA. 

provement  in  that  instrument,  new  tribes  of  insects  or  animalcules 
have  been  revealed  to  the  eye,  still  more  and  more  attenuated.  A 
similar  subordination  might  be  found  in  the  vegetable  kingdom,  and 
in  the  organic  structure  of  both  animals  and  vegetables. 

To  apply  this  analogy  to  the  case  before  us,  we  begin  the  series 
of  inorganic  bodies  with  platinum,  and  descend  through  classes  of 
bodies  constantly  diminishing  in  density,  until  we  come  to  ether, 
the  lightest  of  liquids,  and  on  the  confines  of  those  bodies  which  are 
invisible  to  the  eye,  and  manifested  only  by  the  effects  which  they 
produce.  By  modern  discoveries  the  series  has  been  extended  to 
hydrogen,  a  body  247000  times  lighter  than  platinum.  Here  for  the 
present  we  pause,  standing  in  the  same  relation  with  respect  to  any 
fluids  that  may  lie  beyond,  that  the  ancients  stood  with  respect  to 
common  air,  and  all  the  other  aeriform  fluids. 

Considerations  of  this  nature  lead  us  to  believe  that  there  are>  in 
nature,  fluids  more  subtile  than  hydrogen ;  and,  such  being  the  fact, 
we  can  hardly  resist  the  belief,  that  Heat,  Light  and  Electricity,  are 
bodies  of  this  class, — bodies  which  make  themselves  known  to  us  by 
the  most  palpable  and  energetic  effects,  although  their  own  constitu- 
tion is  too  subtile  and  refined  for  our  organs  to  recognise,  or  our  in- 
struments to  identify  them  as  material. 

418.  Secondly,  in  addition  to  the  foregoing  presumptions,  in  favor 
of  the  supposition  that  electricity  is  a  peculiar  fluid,  it  exhibits  in  itself 
the  properties  of  a  fluid.  The  rapidity  of  its  motions,  the  power  of 
being  accumulated,  as  in  the  Leyden  Jar,  its  unequal  distribution  over 
the  surfaces  of  bodies,  its  power  of  being  confined  to  the  surfaces 
of  bodies  by  the  pressure  of  the  atmosphere,  its  attractions  and  re- 
pulsions, are  severally  properties  which  we  can  hardly  ascribe  to  any 
thing  else  than  an  elastic  fluid  of  the  greatest  tenuity. 

But  granting  the  presence  of  an  elastic  fluid  in  electrical  phe- 
nomena, it  remains  to  be  determined  whether,  according  to  the  hy- 
pothesis of  Franklin,  these  phenomena  are  to  be  ascribed  to  the 
agency  of  a  single  fluid,  or  whether,  according  to  that  of  Du  Fay, 
they  imply  the  existence  of  two  distinct  fluids.  The  numerous  facts 
with  which  the  learner  has  been  made  acquainted  in  the  preceding 
pages,  will  fit  him  to  appreciate  the  evidence  offered  in  favor  of  or 
against  these  hypotheses  respectively. 

29 


226  ELECTRICITY. 

419.  The   principles  of  each  hypothesis   have  been   already  ex- 
plained,  (see  Art.  373.)   and  they  have  been   rendered  familiar  by 
repeated   application.     It  will   be   recollected,   that  they  concur  in 
supposing  that  all  bodies  are  endued  with  a  certain  portion  of  elec- 
tricity, called  their  natural  share,  in  which  the  fluid,   whether  sin- 
gle or  compound,  is  in  a  state  of  perfect  equilibrium  ;  and  that,  in 
the  process  of  excitation,  this  equilibrium  is  destroyed.     But  here 
the  two  views  begin  to  diverge :    the  one  supposes  that  this  equi- 
librium is  destroyed  in  consequence  of  the  separation  of  two  fluids, 
which,  like  an  acid   and  an  alkali  combining  to  form  a  neutral  salt, 
exactly  neutralize  each  other  by  mutual  saturation,  but  which,  when 
separated,  exhibit  their  individual  properties;  the  other,  that  the  equi- 
librium is  destroyed,  like  that  of  a  portion  of  atmospheric  air.  by  great- 
er or  less  exhaustion  on  the  one  side,  or  condensation  on  the  other. 
In  the  former  case,  moreover,  the  equilibrium  is  restored  by  the  re- 
union of  the  two  constituent  fluids ;  in  the  latter,   by  the  movement 
of  the  redundant  portion  to  supply  the  deficient,   as  air  rushes  into 
the  exhausted  receiver  of  an  air  pump. 

It  is  a  remarkable  fact,  that  nearly  every  electrical  phenomenon, 
maybe  perfectly  explained  in  accordance  with  either  hypothesis; 
nor  is  it  agreed,  that  an  experimentum  crucis*  has  yet  been  found. 

420.  One  of  the  latest  advocates  of  the  hypothesis  of  a  single 
fluid  is  Mr.  Singer,   an  able  practical  electrician,   and  the  most  dis- 
tinguished defender  of  the  doctrine  of  two  fluids  is  M.  Biot.     In 
support  of  the  former  doctrine,   are  offered   such  arguments  as  the 
following.     (1.)  Its  greater  simplicity.     It  is  supposed  to  be  more 
conformable  to  the  Newtonian   rule  of  philosophizing,   "  to  ascribe 
no  more  causes  than  are  just  sufficient  to  account  for  the  phenome- 
na."    The  known  frugality  of  nature,   in  all  her  operations,   might 
lead  us  to  suppose,  that  she  would  not  employ  two  agents  to  effect  a 
given  purpose,  when  a  single  agent  would  be  competent  to  its  pro- 
duction.    This  argument,  however,  cannot  be  applied,  either  where 


*  The  "experimentum  crncis,"  is  a  phrase  introduced  by  Lord  Ba- 
con, implying  a  fact  which  can  be  explained  on  one  of  two  opposite 
hypothesis,  and  not  on  the  other.  The  figure  is  derived  from  a  cross 
set  up  where  two  roads  meet,  to  tell  the  traveller  which  road  to  take. 


CAUSE    OF    ELECTRICAL    PHENOMENA.  227 

one  cause  is  not  sufficient  to  account  for  the  phenomena,  or  where 
there  is  direct  proof  of  the  existence  of  more  agents  than  one. 
(2.)  The  appearance  of  a  current,  circulating  from  the  positive  to 
the  negative  surface,  analogous  to  the  passage  of  air  of  greater 
density  into  a  rarefied  space.  This  point  is  much  insisted  on  by 
Singer,  and  numerous  examples  are  brought  forward,  where  the  pro- 
gress of  such  a  current  is  manifest  to  the  senses.  Thus,  the  flame 
of  a  candle,  brought  into  the  circuit  between  the  inside  and  outside 
of  a  Leyden  Jar,  is,  on  the  discharge  of  the  Jar,  bent  towards  the 
negative  side ;  a  pith  ball,  under  similar  circumstances,  moves  in  the 
same  direction ;  when  a  charged  Jar  is  placed  under  the  receiver  of 
an  air  pump,  and  the  air  is  exhausted,  a  luminous  cloud  flows  from 
the  positive  to  the  negative  side,  in  whichever  way  the  Jar  is  electri- 
fied. None  of  these  arguments,  however,  are  found  to  be  conclu- 
sive, for  the  mechanical  effects,  which  are  here  ascribed  to  an  elas- 
tic fluid,  that  is,  the  electric  fluid,  flowing  towards  the  negative  side, 
can  all  be  accounted  for,  either  upon  the  principles  of  attraction  and 
repulsion,  common  to  both  hypotheses,  or  from  the  mechanical  im- 
pulse of  a  current  of  air,  which  is  known  to  be  repelled  from  a  point 
positively  electrified.  The  electric  spark  passing  instantaneously,  or 
at  least  with  a  velocity  entirely  inappreciable,  it  is  impossible  to  de- 
termine its  direction. 

The  fact  that  bodies  negatively  electrified  repel  each  other,  (Art. 
374.)  is  a  strong  argument  against  the  truth  of  the  hypothesis  under 
consideration.  It  is  not  difficult  to  conceive  that  a  self  repellent  fluid 
should  communicate  the  same  property  to  two  pith  balls  in  which  it ' 
resided  ;  but  that  the  mere  deficiency  oCthe  fluid  should  produce  the 
same  effect  is  incredible.  This  fact  drove  ^Epinus,  (a  celebrated 
German  electrician,  who  brought  this  hypothesis  to  the  test  of  Math- 
ematical demonstration,)  to  the  necessity  of  supposing  that  unehctri- 
fied  matter  is  self  repellent, — a  supposition  which  is  not  only  desti- 
tute of  proof,  but  which  is  inconsistent  with  the  general  laws  of  nature, 
from  which  it  appears  that  attraction  and  not  repulsion  exists  mutu- 
ally between  all  kinds  of  bodies.  In  the  distribution  of  electricity 
upon  surfaces  differing  in  shape  and  dimensions,  the  fluid  is  found  to 
arrange  itself  in  strict  accordance  with  hydrostatic  principles,  and 
that  too  in  bodies  negatively  as  well  as  positively  electrified.  Now 
that  the  privation,  or  mere  absence  of  a  fluid,  should  exhibit  such 
properties  of  a  present  fluid,  is  inconceivable. 


228  ELECTRICITY. 

421.  In  favor  of  the  doctrine  of  two  fluids  the  following  arguments 
are  urged.  (1.)  Two  opposite  currents  are  supposed  to  be  some- 
times indicated.  Thus,  (Art.  405.)  a  card  perforated  by  a  strong 
electric  discharge,  exhibits  burs  or  protrusions  on  both  sides.  The 
appearance  of  the  electric  spark,  passing  between  two  knobs,  is  sup- 
posed by  some  writers  to  indicate  the  meeting  of  two  fluids  from 
opposite  parts.  When  the  spark  is  short,  the  whole  distance  between 
the  two  knobs  through  which  it  passes,  is  illuminated.  But  when  the 
spark  is  long,  those  portions  of  it  which  are  nearest  to  the  knobs,  are 
much  brighter  than  the  central  portions.  Near  the  knobs  the  color 
is  white,  but  towards  the  center  of  the  spark  it  is  purplish.  Indeed, 
if  the  spark  is  very  long,  the  middle  part  of  it  is  not  illuminated  at 
all,  or  only  very  slightly.  Now  this  imperfectly  illuminated  part,  is 
obviously  the  spot  where  the  two  electricities  unite,  and  it  is  in  con- 
sequence of  this  union,  that  the  light  is  so  imperfect.  (2.)  The 
two  electricities  are  characterized  by  specific  differences.  The  light 
afforded  by  the  vitreous  surface  is  different  from  that  of  the  resinous ; 
when  the  two  opposite  portions  of  the  spark  meet,  as  above,  the  place 
of  meeting  is  only  half  the  distance  from  the  negative  that  it  is  from 
the  positive  side ;  the  bur  protruded  from  the  card  is  larger  in  the 
direction  of  the  vitreous  than  in  that  of  the  resinous  fluid  ;  and  the 
two  severally  produce  certain  chemical  effects  in  bodies  which  are 
peculiar  to  each.  (3.)  But  the  most  conclusive  argument  in  favor  of 
two  fluids,  is  the  perfect  manner  in  which  this  supposition  accounts 
for  the  distribution  of  electricity  on  bodies  of  different  dimensions. 
On  the  hypothesis  that  electrical  phenomena  are  owing  to  the  agencies 
of  two  fluids,  both  perfectly  incompressible,  the  particles  of  ivhich 
possess  perfect  mobility,  and  mutually  repel  each  other,  while  they 
attract  those  of  the  opposite  fluid,  with  forces  varying  in  the  inverse 
ratio  of  the  squares  of  the  distances,- — on  this  hypothesis,  M.  Poisson, 
a  celebrated  mathematician  of  France,  applied  the  exhaustless  re- 
sources of  the  calculus,  to  determine  the  various  conditions  which 
electricity  would  asswme  in  distributing  itself  over  spheres,  spheroids, 
and  bodies  of  various  figures.  The  results  at  which  he  arrived  were 
such  as  accord  in  a  very  remarkable  degree  with  experiment,  and 
leave  littkfdoubt  that  the  hypothesis  on  which  they  were  built  must 
be  true.  Nor  is  any  supposition  involved  in  the  hypothesis  itself  in- 
consistent with  established  facts.  (4.)  Finally,  authority  is,  at  the 


ATMOSPHERICAL    ELECTRICITY.  229 

present  day,  almost  wholly  on  the  side  of  the  doctrine  of  two  fluids, — 
an  opinion  which  has  constantly  gained  new  adherents  with  every 
new  discovery  in  the  science  of  electricity,  particularly  in  the  depart- 
ment of  Galvanism. 


CHAPTER  V. 

OF  ATMOSPHERICAL   ELECTRICITY.— THUNDER   STORMS.— LIGHT- 
NING RODS. 

422.  Having  learned  the  laws  of  electricity  from  a  great  variety  of 
experiments,  the  student  is  now  prepared  to  look  upon  the  works  of 
nature,  and  to  study  the  phenomena  which  the  same  agent  produces 
there  on  a  most  extensive  scale. 

The  atmosphere  is  always  more  or  less  electrified.  This  fact  is 
ascertained  by  several  different  forms  of  apparatus.  For  the  lower 
regions,  it  is  sufficient  to  elevate  a  metallic  rod  a  few  feet  in  length, 
pointed  at  the  top,  and  insulated  at  the  bottom.  With  the  lower  ex- 
tremity is  connected  an  electrometer,  which  indicates  the  presence 
and  intensity  of  the  electricity.  For  experiments  on  the  electricity 
of  the  upper  regions,  a  kite  is  employed,  not  unlike  a  boy's  kite,  with 
the  string  of  which  is  intertwined  a  fine  metallic  wire.  The  lower 
end  of  the  string  is  insulated  by  fastening  it  to  a  support  of  glass,  or 
by  a  cord  of  silk. 

423.  The  most  powerful  apparatus  ever  employed  for  atmospher- 
ical electricity,   was  constructed   in  France  by  M.  de  Romas.     He 
procured  a  kite  seven  feet  long  and  three  feet  wide,  and  elevated  it  to 
the  height  of  five  hundred  and  fifty  feet.     A  cloud  coming  over,  the 
most  striking  and  powerful  electrical  phenomena  presented  them- 
selves.    Light  straws  that  happened  to  be  on  the  ground  near  the 
string  of  the  kite,  began  to  erect  themselves,  and  to  perform  a  dance 
between  the  apparatus  and  the  ground,  after  the  manner  of  dancing 
images,  as  exhibited  in  ordinary  electrical  experiments.  Art.  386.  (5.) 
At  length  streams  of  fire  began  to  dart  to  the  ground,  some  of  which 
were  an  inch  in  diameter,  and  ten  feet  long,  exhibiting  the  most  ter- 
rific appearance. 

The  foregoing  facts  evince  the  abundance  of  electricity  in  the  at- 
mosphere at  particular  period5 ;  but  experiments  of  a  less  forrnida- 


230  ELECTRICITY. 

ble  kind  have  been  instituted,  to  ascertain  the  electrical  changes  of 
the  air.     For  this  purpose,  Mr.  Canton,  an  English  philosopher,  con- 
structed an  ingenious  apparatus  which  warned  him  of  the  presence 
of  any  unusual   quantity  of  electricity,  by  causing  it  to  ring  a  bell 
connected  with  the  lower  extremity  of  the  apparatus. 

424.  Obvious  as  is  the  connection  between  the  phenomena  of  com- 
mon electrical  apparatus,  and  those  exhibted  in  the  heavens  during 
a  thunder  storm,  yet  the  identity  of  lightning  with  the  electric  spark, 
was  not  dreamed  of  by  the  earlier  electricians.  To  Dr.  Franklin, 
is  universally  conceded  the  merit  of  having  established  this  fact,  first 
by  reasoning  on  just  principles  of  analogy,  and  afterwards  by  actual- 
ly bringing  down  the  lightning  from  the  skies.  The  resemblance 
between  the  appearances  of  lightning  and  electricity,  were  thus  enu- 
merated. 

(1.)  The  zigzag  form  of  lightning  corresponds  exactly  in  appear- 
ance with  a  powerful  electric  spark,  that  passes  through  a  considera- 
ble interval  of  air. 

•  (2.)  Lightning  most  frequently  strikes  such  bodies  as  are  high  and 
prominent,  as  the  summits  of  hills,  the  masts  of  ships,  high  trees, 
towers,  spires,  &c.  So  the  electric  fluid,  when  striking  from  one 
body  to  another,  always  passes  through  the  most  prominent  parts. 

(3.)  Lightning  is  observed  to  strike  most  frequently  into  those  sub- 
stances that  are  good  conductors  of  electricity,  such  as  metals,  water, 
and  moist  substances ;  and  to  avoid  those  that  are  non-conductors. 

(4.)  Lightning  inflames  combustible  bodies ;  the  same  is  effected 
by  electricity. 

(5.)  Metals  are  melted  by  a  powerful  charge  of  electricity  :  this 
phenomenon  is  one  of  the  most  common  effects  of  a  stroke  of  light- 
ning. 

(6.)  The  same  may  be  observed  of  the  fracture  of  brittle  bodies. 

(7.)  Lightning  has  been  known  to  strike  people  blind :  Dr.  Frank- 
lin found,  that  the  same  effect  is  produced  on  animals,  by  a  strong 
electric  charge. 

(8.)  Lightning  destroys  animal  life :  Dr.  Franklin  killed  turkies 
of  abotit  ten  pounds  weight,  by  a  powerful  electric  shock. 

(9.)  The  magnetic  needle  is  affected  in  the  same  way  by  light- 
ning and  by  electricity,. and  iron  may  be  rendered  magnetic  by  both 


ATMOSPHERICAL    ELECTRICITY.  231 

causes.  The  phenomena  therefore  are  strictly  analogous,  and  differ 
only  in  degree  ;  but  if  an  electrified  gun  barrel  will  give  a  spark,  and 
produce  a  loud  report  at  two  inches  distance,  what  effect  may  not  be 
expected  from  10,000  acres  of  electrified  cloud  ?  But  (said  Frank- 
lin,) to  ascertain  the  accuracy  of  these  ideas,  let  us  have  recourse 
to  experiment.  Pointed  bodies  receive  and  transmit  electricity  with 
facility;  let  therefore  a  pointed  metal  rod  be  elevated  into  the  atmos- 
phere, and  insulated  ;  if  lightning  is  caused  by  the  electricity  of  the 
clouds,  such  an  insulated  rod  will  be  electrified  whenever  a  cloud 
passes  over  it ;  this  electricity  may  be  then  compared  with  that  ob- 
tained in  our  experiments. 

425.  Such  were  the  suggestions  of  this  admirable  philosopher;  they 
soon  excited  the  attention  of  the  electricians  of  Europe,  and  having 
attracted  the  notice  of  the  King  of  France,  the  approbation  he  ex- 
pressed excited  in  several  members  of  the  French  Academy,  a  de- 
sire to  perform  the  experiment  proposed  by  Franklin,  and  several  in- 
sulated metallic  rods  were  erected  for  that  purpose.  On  the  10th  of 
May,  1752,  one  of  these,  a  bar  of  iron  forty  feet  high,  situated  in  a 
garden  at  Marly,  became  electrified  during  the  passage  of  a  stormy 
cloud  over  it;  and  during  a  quarter  of  an  hour,  it  afforded  sparks, 
by  which  jars  were  charged,  and  other  electrical  experiments  per- 
formed. During  the  passage  of  the  cloud,  a  loud  clap  of  thunder 
was  heard,  so  that  the  identity  of  these  phenomena  was  thus  com- 
pletely proved.  Similar  experiments  were  made  by  several  electri- 
cians in  England. 

*426.  Doctor  Franklin  had  not  heard  of  these  experiments,  and 
was  waiting  for  the  erection  of  a  spire  at  Philadelphia  to  admit  an  op- 
portunity of  sufficient  elevation  for  his  insulated  rod,  when  it  occur- 
red to  him  that  a  kite  would  obtain  more  ready  access  to  the  re- 
gions of  thunder  than  any  elevated  building.  He  accordingly  ad- 
justed a  silk  handkerchief  to  two  light  strips  of  cedar,  placed  cross- 
wise ;  and  having  thus  formed  a  kite,  with  a  tail  and  loop,  at  the  ap- 
proach of  the  first  storm,  he  repaired  to  a  field  accompanied  by  his 
son.  Having  launched  his  kite  with  a  pointed  wire  fixed  to  it,  he 
waited  its  elevation  to  a  proper  height,  and  then  fastened  a  key  to 
the  end  of  the  hempen  cord,  and  attached  this  by  means  of  a  silk 


232  ELECTRICITY. 

lace  (which  served  to  insulate  the  whole  apparatus)  to  a  post.  The 
first  signs  of  electricity  which  he  perceived,  was  the  separation  of  the 
loose  fibres  of  the  hempen  cord  :  a  dense  cloud  passed  over  the  ap- 
paratus, and  some  rain  falling,  the  string  of  the  kite  became  wet ; 
the  electricity  was  then  collected  by  it  more  copiously,  and  a  knuckle 
being  presented  to  the  key,  a  stream  of  acute  and  brilliant  sparks 
was  obtained.  With  these  sparks,  spirits  were  fired,  jars  charged, 
and  the  usual  electrical  experiments  performed.  Thus  was  the  iden- 
tity of  lightning  and  electricity,  which  had  been  indicated  by  so  many 
analogies,  now  established  by  the  most  decisive  experiments. 

427.  It  is  a  matter  of  much  importance  to  the  science  of  Meteo- 
rology, (Art.  316.)  to  ascertain  from  what  source  atmospherical 
electricity  originates.  Among  the  known  sources  of  this  agent  none 
seems  so  probable,  as  the  evaporation  and  condensation  of  watery 
vapor.  We  have  the  authority  of  two  of  the  most  able  and  accurate 
philosophers,  Lavoisier  and  La  Place,  for  stating  that  bodies'  in  pass- 
ing from  the  solid  or  liquid  state  to  that  of  vapor,  and,  conversely, 
in  returning  from  the  aeriform  condition  to  the  liquid  or  solid  state, 
give  unequivocal  signs  of  either  positive  or  negative  electricity* 

Combustion  is  also  attended  with  the  evolution  of  electricity,  and 
even  the  friction  of  opposite  currents  of  wind,  or  of  a  high  wind 
against  opposing  objects,  probably  generates  more  or  less  of  the  same 
agent.  The  production  of  electricity  during  evaporation  and  con- 
densation may  be  rendered  evident  by  delicate  instruments  ;  as  may 
that  evolved  during  the  friction  of  air.  If  the  stem  of  a  tobacco  pipa 
be  heated  red  hot,  and  a  drop  of  water  be  introduced  by  way  of  the 
bowl,  the  jet  of  steam  falling  on  a  delicate  electrometer,  will  indi- 
cate the  presence  of  electricity. 

It  is  obvious  that  a  cause  which  produces  only  very  feeble  signs  of 
electricity,  in  so  small  a  quantity  of  vapor  as  that  which  arises  from  a 
single  drop  of  water,  may  still  be  sufficient  to  occasion  a  vast  accu- 
mulation of  the  same  agent,  in  such  a  quantity  of  vapor  as  that  which 
is  daily  ascending  into  the  atmosphere.  For  it  has  been  calculated, 
that  *oiore  than  two  thousand  millions  of  hogsheads  of  water  are  evap- 
orated from  the  Mediterranean  alone  in  one  summer's  day. 


THUNDER    STORMS.  233 

Thunder  Storms. 

428.  The  following  are  the  leading  facts  respecting  the  electricity 
of  the  atmosphere  in  relation  to  this  subject,  and  these  are  facts  which 
have  been  established  by  numerous  observers,  of  the  most  accurate 
and  diligent  class.  Beccaria,  an  Italian  electrician,  continued  his  ob- 
servations on  the  electricity  of  the  atmosphere  for  fifteen  years  with 
the  greatest  assiduity ;  and  Cavallo,  Read,  Saussure,  and  others, 
prosecuted  the  same  inquiries  with  similar  zeal. 

(1.)  Thunder  clouds  are,  of  all  atmospheric  bodies,  the  most  high- 
ly charged  with  electricity.  But  all  single,  detached,  or  insulated 
clouds,  are  electrified  in  greater  or  less  degrees,  and  sometimes  posi- 
tively and  sometimes  negatively.  When,  however,  the  sky  is  com- 
pletely overcast  with  a  uniform  stratum  of  clouds,  the  electricity  is 
much  feebler,  than  in  the  single  detached  masses  before  mentioned. 
And,  since  fogs  are  only  clouds  near  the  surface  of  the  earth,  they 
are  subject  to  the  same  conditions ; — a  driving  fog  of  limited  extent, 
is  often  highly  electrified. 

(2.)  The  electricity  of  the  atmosphere  is  strongest  when  hot  weath- 
er succeeds  a  series  of  rainy  days,  or  when  wet  weather  succeeds  a 
series  of  dry  days ;  and  during  any  single  day,  the  air  is  most  elec- 
trical when  the  dew  falls  before  sunset,  or  when  it  begins  to  exhale 
before  sunrise. 

(3.)  In  clear  steady  weather,  the  electricity  generally  remains  pos- 
itive ;  but  in  falling  or  stormy  weather,  it  is  constantly  changing  from 
positive  to  negative,  or  from  negative  to  positive. 

Such  are  the  circumstances  of  atmospheric  electricity  in  general ; 
next,  let  us  attend  to  the  peculiar  phenomena  of  thunder  storms, 
chiefly  as  they  are  exhibited  in  our  own  climate. 

(1.)  In  thunder  storms  there  is  usually  a  singular  and  powerful 
combination  of  all  the  elements, — of  darkness,  rain,  thunder  and  light- 
ning, and  sometimes  hail. 

(2.)  They  occur  chiefly  in  the  hottest  season  of  the  year,  and  after 
mid-day ;  and  are  more  frequent  and  violent  in  warm,  than  in  cold 
coutries. 

(3.)  In  this  State  (Connecticut,)  thunder  storms  usually  come  from 
the  west,  either  directly,  or  from  the  north-west  or  south-west ;  but 
occasionally  from  the  east. 

30 


234  ELECTRICITY. 

(4.)  Violent  thunder  and  lightning  are  frequently  seen  in  volcanoes 
and  water  spouts. 

(5.)  Thunder  storms  sometimes  descend  almost  to  the  surface  of 
the  sea,  and  fall  upon  the  sides  of  mountains ;  in  which  case,  they 
are  extremely  violent. 

(6.)  We  occasionally  observe  the  following  circumstances  succeed 
each  other  in  regular  order :  first,  a  vivid  flash  of  lightning, — then  a 
loud  peal  of  thunder, — and,  after  a  short  interval,  a  sudden  fall  of 
rain,  which  sometimes  stops  as  suddenly  as  it  began. 

429.  There  are  in  thunder  storms  evidently  two  distinct  classes  of 
phenomena  to  be  accounted  for.     The  first  class  consists  of  the  com- 
mon elements  of  a  storm, — clouds,  wind,  and  rain ;  the  second,  of 
thunder  and  lightning.     The  following  proposition  embraces,  in  our 
view,  the  true  explanation  of  both  these  classes  of  phenomena  : — 

The  storm  itself,  including  every  thing  except  the  electrical  appear- 
ances, is  produced  in  the  same  manner  as  other  storms  of  wind  and 
rain  ;  and  the  electricity,  and  of  course  the  thunder  and  lightning, 
is  owing  to  the  rapid  condensation  of  watery  vapor. 

We  do  not,  therefore,  consider  electricity  as  the  cause,  but  as  the 
consequence  of  the  storm ;  or  as  a  concomitant  of  the  clouds,  wind, 
and  rain. 

Lightning  Rods. 

430.  Dr.  Franklin  had  no  sooner  satisfied  himself  of  the  identity 
of  electricity  and  lightning,  than,  with  his  usual  sagacity,  he  conceiv- 
ed the  idea  of  applying  the  knowledge  acquired  of  the  properties  of 
the  electric  fluid,  so  as  to  provide   against  the  dangers  of  thunder 
storms.     The  conducting  power  of   metals,  and  the  influence  of 
pointed  bodies,   to  collect  and  transmit  the  fluid,  naturally  suggested 
the  structure  of  the  Lightning  Rod.     The  experiment  was  tried  and 
has  proved  completely  successful ;  and  probably  no  single  application 

of  scientific  knowledge  ever  secured  more  celebrity  to  its  author. 

tf 

431.  Lightning  rods  are  at  present  usually  constructed  of  wrought 
iron  about  three  fourths  of  an  inch  in  diameter.     The  parts  may  be 
made  separate,  but,  when  the  rod  is  in  its  place,  they  should  be 


LIGHTNING    RODS.  235 

screwed  together  so  as  to  fit  closely,  and  to  make  a  continuous  sur- 
face, since  the  fluid  experiences  much  resistance  in  passing  through 
links  and  other  interrupted  joints.  At  the  bottom  the  rod  should  ter- 
minate in  two  or  three  branches,  going  off  in  a  direction  from  the 
building.  The  depth  to  which  it  enters  the  earth  should  not  be  less 
than  five  feet ;  but  the  necessary  depth  will  depend  somewhat  on  the 
nature  of  the  soil :  wet  soils  require  a  less,  and  dry  soils  a  greater 
depth.  In  dry  sand  it  must  not  be  less  than  ten  feet ;  and  in  such 
situations,  it  would  be  better  still  to  connect,  by  a  convenient  conduc- 
ting communication,  the  lower  end  of  the  rod  with  a  well  or  spring  of 
water.  It  is  useful  to  fill  up  the  space  around  the  part  of  the  rod  that 
enters  the  ground,  with  coarsely  powdered  charcoaal,  which  at  once 
furnishes  a  good  conductor,  and  preserves  the  metal  from  corrosion. 
The  rod  should  ascend  above  the  ridge  of  the  building  to  a  height 
determined  by  the  following  principle  :  that  it  will  protect  a  space  in 
every  direction  from  it,  whose  radius  is  equal  to  twice  its  height.  It 
is  best,  when  practicable,  to  attach  it  to  the  chimney  ;  which  needs 
peculiar  protection,  both  on  account  of  its  prominence,  and  because 
the  products  of  combustion,  smoke,  watery  vapor,  &LC.  are  conduc- 
tors of  electricity.  For  a  similar  reason  a  kitchen  chimney,  being 
that  in  which  the  fire  is  kept  during  the^ season  of  thunder  storms, 
requires  to  be  especially  protected.  The  rod  is  terminated  above  in 
three  forks,  each  of  which  ends  in  a  sharp  point.  As  these  points 
are  liable  to  have  their  conducting  power  impaired  by  rust,  they  are 
protected  from  corrosion  by  being  covered  with  gold  leaf;  or  they 
may  be  made  of  solid  silver  or  platina.  Black  paint  being  made  of 
charcoal,  it  forms  a  better  coating  for  the  rod  than  paints  made  of 
other  colors,  the  bases  of  which  are  worse  conductors.  The  rod 
may  be  attached  to  the  building  by  wooden  stays.  Iron  stays  are 
sometimes  employed,  and  in  most  cases  they  would  be  safe,  since 
electricity  pursues  the  most  direct  route ;  but  in  case  of  an  extraordi- 
nary charge,  there  is  danger  that  it  will  divide  itself,  a  part  passing 
into  the  building  through  the  bolt,  especially  if  this  terminates  in  a 
point.  Buildings  furnished  with  lightning  rods  have  occasionally  been 
struck  with  lightning  ;  but  on  examination  it  has  generally,  if  not  al- 
ways, been  found  that  the  structure  of  the  rod  was  defective ;  or 
that  too  much  space  was  allotted  for  it  to  protect.  When  the  fore- 
going rules  are  observed  the  most  entire  confidence  may  be  reposed 
in  this  method  of  securing  safety  in  thunder  storms. 


236  ELECTRICITY. 


CHAPTER  VI. 

PRECAUTIONS  FOR  SAFETY    DURING  THUNDER  STORMS— ANIMAL 
ELECTRICITY— CONCLUDING  REMARKS. 

432.  The  great  number  of  pointed  objects  that  rise  above  the  gen- 
eral level,  in  a  large  city,  have  the  effect  to  dissipate  the  electricity  of 
a  thunder  cloud,  and  to  prevent  its  charge  from  being  concentrated 
on  any  single  object.     Hence  damage  done  by  lightning  is  less  fre- 
quent in  a  populous  town,  than  in  solitary  buildings.     For  similar 
reasons,  a  great  number  of  ships,  lying  at  the  docks,  disarm  the  light- 
ning of  its  power,  and  thus  avert  the  injury  to  which  the   form  of 
their  masts  would  otherwise  expose  them.     A  solitary  ship  on  the 
ocean  unprotected  by  conductors,  would  appear  to  be  peculiarly  in 
danger  from  lightning ;  but  while  the  greater  number  of  ships  that 
traverse  the  ocean  are  wholly  unprotected,  accidents  of  this  kind  are 
comparatively  rare.     The  reason  probably  is,  that  water  being  a  bet- 
ter conductor  than  wood,  the  course  of  the  discharge  towards  the 
water  is  not  easily  diverted,  and  will  not  take  the  mast  in  its  way  un- 
less the  latter  lies  almost  directly  in  its  course.— Barns  are  peculiarly 
liable  to  be  struck  with  lightning,  and  to  be  set  on  fire ;  and  as  this 
occurs  at  a  season  when  they  are  usually  filled  with  hay  and  grain,  the 
damage  is  more  serious,  for  the  quantity  of  combustible  matter  they 
contain  is  such  as  to  render  the  fire  unmanageable. 

433.  Silk  dresses  are  sometimes  worn  with  the  view  of  protec- 
tion by  means  of  the  insulation  they  afford.     They  cannot,  however, 
be  deemed  very  effectual  unless  they  completely  envelop  the  person ; 
for  if  the  head  and  the  extremities  of  the  limbs  be  exposed,   they 
will  furnish  so  many  avenues  to  the  fluid  as  to  render  the  insulation 
of  the  other  parts  of  the  system  of  htlle  avail.     The  same  remark 
applies  to  the  supposed   security  that  is  obtained   by  sleeping  on  a 
feather  bed.     Were  the  person  situated  within  the  bed,   so  as  to  be 
entirely  enveloped  by  the  feathers,  they  would  afford  some  protec- 
tion ;  but  if  the  person  be  extended  on  the  surface  of  the  bed,  in 
the  usual  posture,  with  the  head  and  feet  nearly  in  contact  with  the 
bedsted,  he  would  rather  lose  than  gain  by  the  non-conducting  prop- 
erties of  the  bed ;  since,  being  a  better  conductor  than  the  bed,  the 
charge  would  pass  through  him  in  preference  to  that.     The  horizon- 


SAFETY    DURING    THUNDER    STORMS.  237 

tal  posture,  however,  is  safer  than  the  erect ;  and  if  any  advantage 
on  the  whole  is  gained  by  lying  in  bed  during  a  thunder  storm,  it 
probably  arises  from  this  source.  The  same  principle  suggests  a 
reason  why  men  or  animals  are  so  frequently  struck  with  lightning 
when  they  take  shelter  under  a  tree  during  a  thunder  storm.  The 
fluid  first  strikes  the  tree,  in  consequence  of  its  being  an  elevated 
and  pointed  object,  but  it  deserts  the  tree  on  reaching  the  level  .of 
the  man  or  animal,  because  the  latter  is  a  better  conductor  than 
the  tree. 

Tall  trees  situated  near  a  dwelling  house,  furnish  a  partial  protec- 
tion to  the  building,  being  both  better  conductors  than  the  materials 
of  the  house,  and  having  the  advantage  of  superior  elevation. 

434.  The  protection  of  chimneys  is  of  particular  importance,  for 
to  these  a  discharge  is  frequently  determined.  When  a  fire  is  burn- 
ing in  the  chimney,  the  vapor,  smoke,  and  hot  air,  which  ascend  from 
it  furnish  a  conducting  medium  for  the  fluid ;  but  even  when  no  fire 
is  burning,  the  soot  that  lines  the  interior  of  a  chimney,  is  a  good  con- 
ductor, and  facilitates  the  passage  of  the  discharge. 

It  is  quite  essential,  during  a  thunder  storm,  to  avoid  every  con- 
siderable mass  of  water,  and  even  the  streamlets  that  have  resulted 
from  a  recent  shower ;  for  these  are  all  excellent  conductors,  and  the 
height  of  a  human  being,  when  connected  with  them,  is  very  likely 
to  determine  the  course  of  an  electric  discharge.  The  partial  con- 
ductors, through  which  the  lightning  directs  its  course,  when  it  enters 
a  building,  are  usually  the  appendages  of  the  walls  and  partitions ; 
the  most  secure  situation  is  therefore  the  middle  of  the  room,  and 
this  situation  may  be  rendered  still  more  secure  by  standing  on  a  glass 
legged  stool,  a  hair  mattress,  or  even  a  thick  woollen  rug.  The  part 
of  every  building  least  liable  to  receive  injury,  is  the  middle  story, 
as  the  lightning  does  not  always  pass  from  the  clouds  to  the  earth, 
but  is  occasionally  discharged  from  the  earth  to  the  clouds.  Hence 
it  is  absurd  to  take  refuge  in  a  cellar,  or  in  the  lowest  story  of  a 
house ;  and  many  instances  are  on  record  in  which  the  basement 
story  has  been  the  only  part  of  the  building  that  has  sustained  severe 
injury.  Whatever  situation  be  chosen,  any  approach  to  the  fire  place 
should  be  particularly  avoided.  An  open  door  or  window  is  an  un- 
safe situation,  because  the  lightning  is  apt  to  traverse  the  large  tim- 


238  ELECTRICITY. 

bers  that  compose  the  frame  of  the  house,  and  would  be  determined 
towards  the  animal  system  on  account  of  its  being  a  better  conductor. 
In  a  carriage  the  passenger  is  safer  in  the  central  part  than  next  to  the 
walls ;  but  a  carriage  may  be  effectually  protected  by  attaching  to  its 
upper  surface  metallic  strips  connected  with  the  wheel  tire.  The 
fillets  of  silver  plating  which  are  frequently  bound  round  the  carriage, 
may  be  brought  into  the  conducting  circuit. 

Animal  Electricity. 

435.  Of  the  natural  agencies  of  electricity,  one  of  the  most  re- 
markable, is  that  exhibited  by  certain  species  of  fish,  especially  the 
Torpedo  and  the  Gymnotus.     This  peculiar  property  of  the  Torpe- 
do was  known  to  the  ancient  naturalists,  and  is  accurately  described 
by  Aristotle  and  by  Pliny.    Aristotle  says  that  this  fish  causes  or  pro- 
duces a  torpor  upon  those  fishes  it  is  about  to  seize,  and  having  by 
that  means  got  them  into  its  mouth,  it  feeds  upon  them.     Pliny  says 
that  this  fish,  if  touched  by  a  rod  or  spear,  even  at  a  distance,  para- 
lyzes the  strongest  muscles. 

436.  The  fact,  however,  that  this  extrordinary  power  depended 
upon  electricity,  was  not  known  until  about  the  year  1773,  when  it 
was  ascertained  by  Mr.  Walsh,  that  the  Torpedo  was  capable  of  giv- 
ing shocks  to  the  animal  system,  analogous  to  those  of  the  Leyden 
Jar.     Though  this  property  is  regarded  as  establishing  the  identity  of 
the  power  with  the  electric  fluid,  yet  this  power,  as  developed  in  the 
Torpedo,  has  never  been  made  to  afford  a  spark,  nor  to  produce  the 
least  effect  upon  the  most  delicate  electrometer.     As  late  as  the  year 
1828,  experiments  were  made  upon  the  Torpedo,  by  Sir  Humphry 
Davy,  and  the  conclusions  to  which  he  arrived,  were  that  the  electri- 
city resides  in  this  animal  in  a  form  suited  exclusively  to  the  purpose 
of  communicating  shocks  to  the  animal  system,  while  it  has  little  or 
nothing  else  in  common  with  the  properties  of  electricity,  as  develop- 
ed in  various  artificial  arrangements. 

The  Torpedo  is  a  flat  fish,  seldom  twenty  inches  in  length,  but  one 
fouE^J  on  the  British  coast  was  four  and  a  half  feet  long.  The  elec- 
tricity of  the  Torpedo  has  the  same  relation  as  common  electricity  to 
bodies  in  respect  to  their  conducting  power,  being  readily  transmitted 
through  metals,  water,  and  other  conductors,  and  not  being  transmit- 
ted through  glass,  and  other  non-conductors. 


ANIMAL    ELECTRICITY. 


239 


437.  The  electric  organs  of  the  Torpedo  are  two  in  number,  and 
placed  one  on  each  side  of  the  cranium  and  gills.     The  length  of 
each  organ  is  somewhat  less  than  one  third  part  of  the  length  of  the 
whole  animal.  Each  organ  consists  of  perpendicular  columns  reaching 
from  the  under  to  the  upper  surface  of  the  body,  and  varying  in  length 
according  to  the  various  thickness  of  the  flesh  in  different  parts.    The 
number  of  these  columns  are  not  constant,  being  not  only  different 
in  different  Torpedos,  but  likewise  in  different  ages  of  the  animal, 
new  ones  seeming  to  be  produced  as  the  animal  grows.     In  a  very 
large  Torpedo,  one  electric  organ  has  been  found  to  consist  of  one 
thousand  one  hundred  and  eighty  two  columns.     The  diameter  of  a 
column  is  about  one  fifth  of  an  inch.    Each  column  is  divided  by  hori- 
zontal partitions,  consisting  of  transparent  membrane,  placed  over 
each  other  at  very  small  distances,  and  forming  numerous  inter- 
stices, which  appear  to  contain  a  fluid.     The  number  of  partitions 
contained  in  a  column  one  inch  in  length,  has  been  found  in  some  in- 
stances not  less  than  one  hundred  and  fifty.     By  this  arrangement, 
the  amount  of  electrified  surface  is  exceedingly  great ;  equivalent, 
in  one  instance,  to  one  thousand  and  sixty  four  feet  of  coated  glass. 
Hence,  the  effects  of  the  electricity  of  the  Torpedo  are  such  as  cor- 
respond to  those  which,  in  artificial  arrangements,   are  produced  by 
diffusing  a  given  quantity  of  fluid  over  a  great  surface,   by  which  its 
intensity  is  much  diminished. 

438.  The  Gymnotus,  or  Surinam  eel,  is  found   in  the  rivers  of 
South  America.     It  ordinary  length  is  from  three  to  four  feet ;  but 
they  are  said  to  be  sometimes  twenty  feet  long,  and  to  give  a  shock 
that  is  instantly  fatal.     The  electrical  organs  of  the  Gymnotus,  con- 
stitute  more  than  one  third  part  of  the  whole  animal ;  they  consist 
of  two  pairs,  of  different  sizes  and  placed  on  different  sides.     The 
shock  communicated  to  fishes  instantly  paralyzes  them,  so  that  they 
become  the  prey  of  the  Gymnotus.     By  irritating  the  animal  with 
one  hand   while  the  other  is  held  at  some  distance  in  the  water,  a 
shock  is  received,  as  severe  as  that  of  the  Leyden  Jar. 

Unlike  the  Torpedo,  the  Gymnotus  gives  a  small  but  perceptible 
spark,  affording  additional  proof  of  the  identity  of  the  power  with 
that  of  electricity. 


240  ELECTRICITY. 

JVL  Humboldt,  in  his  travels  in  South  America,  describes  a  sin- 
gular method  of  catching  the  Gymnotus,  by  driving  wild  horses  into 
a  lake  which  abounds  with  them.  The  fish  are  weaned  or  exhaust- 
ed by  their  efforts  against  the  horses,  and  then  taken ;  but  such  is 
the  violence  of  the  charge  which  they  give,  that  some  of  the  horses 
are  drowned  before  they  can  recover  from  the  paralyzing  shocks  of 
the  eels. 

The  Silurus  electricus,  is  a  fish  found  in  some  of  the  rivers  of 
Africa.  Its  electrical  powers  are  inferior  to  those  of  the  Torpedo 
and  Gymnotus,  but  they  are  still  sufficient  to  give  a  distinct  shock  to 
the  human  system. 

439.  Certain  furred  animals,  particularly  the  cat,  become  sponta- 
neously electrified.  This  is  more  especially  observable  on  cold  windy 
nights,  when  the  state  of  the  air  is  favorable  to  insulation.  At  such 
times  a  cat's  back  will  frequently  afford  electrical  sparks.  Ancient 
historians  mention  a  number  of  very  remarkable  occurrences,  of  good 
or  evil  omen,  which  are  due  to  the  electricity  of  the  atmosphere. 
Herodotus  informs  us  that  the  Thracians  disarmed  the  sky  of  its 
thunder,  by  throwing  their  arms  into  the  air ;  and  that  the  Hyperbo- 
reans produced  the  same  effect,  by  launching  among  the  clouds  darts 
armed  with  points  of  iron.  Caesar  in  his  Commentaries,  says  that  in 
the  African  war,  after  a  tremendous  storm  which  threw  the  whole  of 
the  Roman  army  into  great  disorder,  the  points  of  the  darts  of  a  great 
number  of  the  soldiers  shone  with  a  spontaneous  light.  In  the  month 
of  February  (says  he)  about  the  second  watch  of  the  night,  there  sud- 
denly arose  a  great  cloud,  followed  by  a  dreadful  storm  of  hail,  and 
in  the  same  night  the  points  of  the  darts  of  the  fifth  legion  appeared 
on  fire. 

During  a  dry  snow  storm,  when  electricity  is  evolved  in  great  quan- 
tities, and,  on  account  of  the  dry  state  of  the  air,  is  partially  insula- 
ted on  conducting  bodies,  similar  appearances  are  exhibited.  Thus 
the  ears  of  horses  and  various  pointed  bodies  emit  faint  streams  of 
light.  These  phenomena  are  sometimes  exhibited  in  a  most  striking 
manner  in  a  storm  at  sea,  when  the  masts  of  a  ship,  yard  arms,  and 
every  other  pointed  object  are  tipped  with  lightning. 


CONCLUDING    REMARKS. 

Concluding  Remarks. 

440.  From  the  energy  which  electricity  displays  in  our  experi- 
ments, and  much  more  in  thunder  storms,  there  can  be  no  question 
that  it  holds  an  important  rank  among  the  ultimate  causes  of  natural 
phenomena.  Its  actual  agencies,  however,  are  liable  to  be  misinter- 
preted, and  that  they  have  been  so  in  fact,  is  too  manifest  from  the 
history  of  the  science.  After  the  splendid  experiments  with  the 
Leyden  Jar,  and  more  especially,  after  the  indentity  of  electricity 
with  lightning  had  been  proved,  electricians  fancied  that  they  had  dis- 
covered the  clue  which  would  conduct  them  safely  through  the  laby- 
rinth of  nature.  Every  thing  not  before  satisfactorily  accounted  for, 
was  now  ascribed  to  electricity.  They  saw  in  it  not  only  the  cause 
of  thunder  storm,  but  of  storms  in  general ;  of  rain,  snow,  and  hail ; 
of  whirlwinds  and  water  spouts ;  of  meteors  and  the  aurora  borealis ; 
and  finally,  of  tides  and  comets  and  the  motions  of  the  heavenly 
bodies.  Later  electricians  have  found  in  the  same  agent  the  main 
spring  of  animal  and  vegetable  life,  and  the  grand  catholicon  which 
cures  all  diseases.  Recent  attempts  have  been  made  to  establish 
the  very  identity  of  galvanic  electricity  and  the  nervous  influence,  by 
which  the  most  important  functions  of  animal  life  are  controlled. 

Among  the  most  important  of  the  agencies  of  electricity  in  the 
economy  of  nature,  is  that  which,  according  to  the  views  of  Sir 
Humphry  Davy,  it  sustains  in  relation  to  the  chemical  agencies  of 
bodies.  Chemical  and  electrical  attraction,  he  supposes,  are  one 
and  the  same  thing,  or  at  least  dependent  on  the  same  cause,  the  at- 
traction between  the  elements  of  a  compound  arising  solely  from 
their  being  naturally  in  opposite  electrical  states.  But  the  discus- 
sion of  this  hypothesis  belongs  more  appropriately  to  Galvanism,  at 
branch  of  our  subject  which  on  account  of  its  peculiarities,  especial- 
ly in  the  mode  of  excitation,  has  been  constituted  a  separate  depart- 
nientof  science. 


242 


PART  V.- 


GENERAL  PRINCIPLES. 

44  J.  MAGNETISM  is  the  science  which  treats  of  the  properties  and 
effects  of  the  magnet. — The  same  term  is  also  used  to  denote  the 
unknown  cause  of  magnetic  phenomena ;  as  when  we  speak  of  mag- 
netism as  excited,  imparted,  and  so  on. 

Magnets  are  bodies,  either  natural  or  artificial,  which  have  the 
property  of  attracting  iron,  and  the  power,  when  freely  suspended, 
of  taking  a  direction  towards  the  poles  of  the  earth. 

The  natural  magnet  is  sometimes  called  the  loadstone.*  It  is  an 
oxide  of  iron  of  a  peculiar  character,  found  occasionally  in  beds  of 
iron  ore.  Though  commonly  met  with  in  irregular  masses  only  a  few 
inches  in  diameter,  yet  it  is  sometimes  found  of  a  much  larger  size. 
One  recently  brought  from  Moscow  to  London,  weighed  one  hun- 
dred and  twenty  five  pounds,  and  supported  more  than  two  hundred 
pounds  of  iron. 

442.  The  attractive  powers  of  the  loadstone  have  been  known 
from  a  high  antiquity,  and  are  mentioned  by  Homer,  Pythagoras,  and 
Aristotle.  But  the  directive  powers  were  not  known  in  Europe,  un- 
til the  thirteenth  century,  when  they  were  discovered  by  a  Neapolitan 
named  Flavio;  though  some  writers  have  endeavored  to  trace  the  his- 
tory of  the  compass  needle  to  a  remoter  period,  and  some  have  stren- 
uously maintained  that  the  Chinese  were  in  possession  of  it  many 
centuries  before  it  was  known  to  Europeans. 

Magnetism  is  the  most  recent  of  all  the  physical  sciences,  and  not- 
withstanding the  numerous  discoveries  achieved  in  it  within  a  few 
years,  and  the  remarkable  precision  with  which  its  laws  have  been 
ascertained,  yet  it  is  still  to  be  regarded  as  a  science  quite  in  its  in- 
fancy, although  it  is  rapidly  progressive. 
•V 

*  SaiJ  to  be  derived  from  Icedan,  a  Saxon  word  which  signifies  to 
guide. 


GENERAL    PRINCIPLES. 


243 


443.  If  a  magnet  be  rolled  in  iron  filings,  it  will  attract  them  to 
itself.  This  effect  takes  place  especially  at  two  opposite  points, 
where  a  much  greater  quantity  of  the  filings  will  be  collected  than 
in  any  other  parts  of  the  body.  The  two  opposite  points  in  a  mag- 
net,- where  its  attractive  powers  ap-  Fig.  86. 
pear  chiefly  to  reside,  are  called  its 
poles.  The  straight  line  which  joins 
the  poles,  is  called  the  axis. 

If  a  large  sewing  needle  or  small  bar  of  steel  be  rubbed  on  the 
loadstone,  one  extremity  on  one  pole,  and  the  other  extremity  on 
the  other,  the  needle  or  bar  will  itself  become  a  magnet,  capable  of 
exhibiting  all  the  properties  of  the  loadstone.  Without  staying  at 
present  to  describe  more  minutely  the  process  of  making  artificial 
magnets,  we  will  suppose  ourselves  provided  with  several  magnetic 
needles  and  bars,  and  we  may  proceed  with  them  to  study  the  leading 
facts  of  the  science  of  magnetism.  By  attaching  a  fine  thread  to  the 
middle  of  a  needle,  and  suspending  it  so  as  to  move  freely  in  a  hori- 
zontal plane  ;  or  by  resting  it  on  a  point,  as 
is  represented  in  figure  87,  we  shall  have  ~ 
a  simple  and  convenient  apparatus  for  nu- 
merous experiments.  The  needle  thus  sus- 
pended will  place  itself  in  a  direction  near- 
ly, though  not  exactly,  north  and  south.  If 
the  needle  is  drawn  out  of  the  positiqn  it  assumes  when  at  rest  it  will 
vibrate  on  either  side  of  that  position  until  it  finally  settles  in  the  same 
line  as  before,  one  pole  always  returning  towards  the  north,  and  the 
other  towards  the  south.  Hence  the  two  poles  are  denominated  re- 
spectively north  and  south  poles.  In  magnets  prepared  for  experi- 
ments, these  poles  are  marked  either  by  the  letter  N  and  S,  or  by  a 
line  drawn  across  the  magnet  near  one  end,  which  denotes  that  the 
adjacent  pole  is  the  north  pole. 

444.  By  means  of  the  foregoing  apparatus  we  may  ascertain  that 
the  magnet  has  the  following  general  properties,  viz. 

First,  powers  of  attraction  and  repulsion. , 

Secondly,  the  power  of  communicating  magnetism  to  iron  or  steel 
by  induction. 

Thirdly,  polarity  or  the  power  of  taking  a  direction  towards  the 
poles  of  the  earth. 


244  MAGNETISM, 

Fourthly,  the  power  of  inclining  itself  towards  a  point  below  the 
horizon,  usually  denominated  the  dip  of  the  needle. 

The  farther  developement  of  these  properties  will  constitute  the 
subjects  of  the  following  chapters. 


CHAPTER  I. 

OF  MAGNETIC  ATTRACTION. 

445.  When  either  pole  of  a  magnet  is  brought  near  to  a  piece 
of  iron,  a  mutual  attraction  takes  place  between  them. 

Thus,  when  the  ends  of  a  magnetic  bar  or  needle  are  dipped  into 
a  mass  of  iron  filings,  these  adhere  in  a  cluster  to  either  pole.  A  bar 
of  soft  iron,  or  a  piece  of  iron  wire,  resting  on  a  cork,  and  floating  on 
the  surface  of  water  or  quicksilver,  may  be  led  in  any  direction  by 
bringing  near  to  it  one  of  the  poles  of  a  magnet.  This  action  is 
moreover  reciprocal,  that  is,  the  iron  attracts  the  magnet  with  the 
same  force  that  the  magnet  attracts  the  iron.  If  the  two  bodies  be 
placed  on  separate  corks  and  floated,  they  will  approach  each  other 
with  equal  momenta ;  or  if  the  iron  be  held  fast,  the  magnet  will 
move  towards  it. 

446.  Two  other  metals  beside  iron,  namely,  nickel  and  cobalt, 
are  susceptible  of  magnetic  attraction.     These  metals,  however,  ex- 
ist in  nature  only  in  comparatively  small  quantities,  and  therefore  by 
magnetic  bodies,  are  usually  intended  such  as  are  ferruginous.     Even 
iron,  in  some  of  its  combinations  with  other  bodies,  loses  its  magnetic 
properties ;  only  a  few  of  the  numerous  ores  of  iron  are  attracted  by 
the  magnet.     But  soft  metallic  iron,  and  some  of  the  ores  of  the 
same  metal,  affect  the  needle  even  when  existing  in  exceedingly  small 
quantities,  so  that  the  magnet  becomes  a  very  delicate  test  of  the  pres- 
ence of  iron.     Compass  needles  are  sometimes  said  to  be  disturbed 
by  the  minute  particles  of  steel  left  in  the  dial  plate  by  the  graver ; 
and  the  proportion  of  iron  in  some  minerals  may  be  exactly  estima- 
ted by  the  power  they  exert  upon  the  needle. 

*'» 

•   447.  In  the  action  of  magnets  on  each  other,  poles  of  the  same 
name  repel,  those  of  different  names  attract  each  other. 


MAGNETIC    ATTRACTION.  245 

Thus  the  north  pole  of  one  magnet  will  repel  the  north  pole  of  the 
other,  and  attract  its  south  pole.  The  south  pole  of  one  will  repel 
the  south  pole  of  the  other  and  attracts  its  north  pole.  These  effects 
it  will  be  perceived,  are  analogous  to  those  produced  by  the  two  spe- 
cies of  electricity  ;  and  they  equally  imply  two  species  of  magnetism 
or  two  magnetic  fluids  (as  it  is  convenient  to  call  them)  namely,  the 
northern,  and  the  southern,  or  as  they  are  now  denominated  the  bo- 
real and  the  austral  fluids. 

448.  By  bringing  a  magnet  near  to  iron  or  steel,  the  latter  is  ren- 
dered magnetic  by  Induction. 

Thus,  let  the  north  pole  of  a  FiS-  88> 

magnetic  bar  A,  (Fig.  88.)  be 
brought  near  to  one  end  of  an  un- 
magnetized  bar  of  soft  iron  B :  the 
iron  will  immediately  become  it- 
self a  magnet,  capable  of  attracting  iron  filings,  having  polarity  when 
suspended  and  possessing  the  power  of  communicating  the  same 
properties  to  other  pieces  of  iron.  It  is,  however,  only  while  the  iron 
remains  in  the  vicinity  of  the  magnet,  that  it  is  endued  with  these  pro- 
perties ;  for  let  the  magnet  be  withdrawn  and  it  loses  at  once  all  the 
foregoing  powers.  This,  it  will  be  remarked  is  asserted  of  soft  iron ; 
for  steel  and  hardened  iron  are  differently  affected  by  induced  mag- 
netism. 

On  examining  the  kind  of  magnetism  induced  upon  the  two  ends 
of  the  iron  bar  B,  (Fig.  88.)  which  we  may  easily  do  by  bringing 
near  it  the  poles  of  the  needle,  (Fig.  87.)  we  shall  find  that  the  near- 
er end  has  south,  and  the  remoter  end  north  polarity.  This  effect 
also  is  analogous  to  that  produced  by  electrical  induction.  A  corres- 
ponding effect  would  have  taken  place,  had  the  south  instead  of  the 
north  pole  of  the  magnet  been  presented  to  the  bar  of  iron ;  in  which 
case  the  nearer  end  would  have  exhibited  northern,  and  the  re- 
mote end  southern  polarity.  Or,  to  express  this  important  proposi- 
tion in  general  terms, 

Each  pole  of  a  magnet  induces  the  opposite  kind  of  polarity  in  that 
end  of  the  iron  which  is  nearest  to  it,  and  the  same  kind  in  that  end 
which  is  most  remote. 


2445  MAGNETISM. 

449.  The  power  of  a  magnet  is  increased,  by  the  exertion  of  its  in- 
ductive power  upon  a  piece  of  iron  in  its  neighborhood. 

The  end  of  the  piece  of  iron  contiguous  to  the  pole  of  the  mag- 
net, is  no  sooner  endued  with  the  opposite  polarity,  than  it  re-acts 
upon  the  magnet  and  increases  its  intensity,  and  a  series  of  actions 
and  re-actions  take  place  between  the  two  bodies,  similar  to  what  oc- 
curs in  electrical  induction.  On  this  account  the  powers  of  a  mag- 
net are  increased  by  action,  and  impaired  or  even  lost  by  long  disuse. 
By  adding,  from  time  to  time,  small  pieces  of  iron  to  the  weight  ta- 
ken up  by  a  magnet,  its  powers  may  be  augmented  greatly  beyond 
their  original  amount.  Hence,  the  force  of  attraction  of  the  dissim- 
ilar poles  of  two  magnets,  is  greater  than  the  force  of  repulsion  of 
the  similar  poles ;  because,  when  the  poles  are  unlike,  each  contri- 
butes to  enhance  the  power  of  the  other,  but  when  they  are  alike, 
the  influence  which  they  reciprocally  exert,  tends  to  make  them  un- 
like, and  of  course  to  impair  their  repulsive  energies. 

Hence,  also  a  strong  magnet  has  the  power  of  reversing  the  poles 
of  a  weak  one.  Suppose  the  north  pole  of  the  weaker  body  to  be 
brought  into  contact  with  the  north  pole  of  the  stronger ;  the  latter 
will  expel  north  polarity,  or  the  boreal  fluid,  and  attract  the  austral, 
a  change  which  in  certain  cases  will  be  permanent. 

If  the  north  pole  of  a  magnetic  bar  be  placed  upon  the  middle  of 
an  iron  bar,  the  two  ends  of  the  latter  will  each  have  north  polarity 
while  the  part  of  the  bar  immediately  in  contact  with  the  magnet  re- 
ceives south  polarity ;  and  if  the  same  north  pole  be  placed  on  the 
center  of  a  circular  piece  of  iron,  all  parts  of  the  circumference  will 
be  endued  with  north  polarity  while  the  plate  will  have  a  south  pole 
in  the  center.  By  cutting  the  plate  into  the  form  of  a  star,  each  ex- 
tremity of  the  radii  becomes  a  weak  north  pole  when  the  north  pole 
of  a  magnet  is  placed  in  the  center  of  the  star.  If  an  iron  bar  is 
placed  between  the  dissimilar  poles  of  two  magnetic  bars,  both  of  the 
magnets  will  conspire  to  increase  the  intensity  of  each  pole  of  the  bar 
and  the  magnetism  imparted  to  the  bar  will  be  considerably  stronger 
than, from  either  magnet  alone;  but  if  the  same  bar  be  placed  between 
the  two  similar  poles,  the  opposite  polarity  will  be  imparted  to  each 
end,  while  the  same  polarity  is  given  to  the  center  of  the  bar.  Thus 
if  the  bar  be  placed  between  the  north  poles  of  two  magnets,  each 


MAGNETIC    ATTRACTION.  247 

end  of  the  bar  will  become  a  south  pole  and  the  center  a  north  pole. 
When  one  end  of  a  magnetic  bar  is  applied  to  the  ends  of  two  or 
more  wires  or  sewing  needles,  the  latter  arrange  themselves  in  radii 
diverging  from  the  magnetic  pole.  This  effect  is  in  consequence  of 
their  remoter  ends  becoming  endued  with  similar  polarity,  and  repel- 
ling each  other.  A  like  effect  is  observable  among  the  filaments  of 
iron  filings,  that  form  a  tuft  on  the  end  of  a  magnetic  bar. 

450.  The  foregoing  experiments  are  sufficient  to  show  that  when 
a  piece  of  iron  is  attracted  by  the  magnet,  it  is  first  itself  converted 
into  a   magnet  by  the  inductive  influence  of  the  magnetising  body. 
Each  of  the  iron  filings  which  compose  the  tuft  at  the  pole  of  a  mag- 
netic bar  or  needle,  is  itself  a  magnet  and  in  consequence  of  being 
such,  induces  the  same  property  in  the  next  particle  of  iron,  and  that 
in  the  next,  and  so  on  to  the  last.     Hence  magnetic  attraction  does 
not  exist,  strictly  speaking,  between  a  magnet  and  iron,  but  only  be- 
tween the  opposite  poles  of  magnets ;  for  the  iron  must  first  become 
a  magnet  before  it  is  capable  of  magnetic  influence. 

451.  Soft  iron  readily  acquires  magnetism  and  as  readily  loses  it ; 
hardened  steel  acquires  it  more  slowly,  but  retains  it  permanently. 

In  the  preceding  examples,  the  magnetism  acquired  by  a  bar  of 
iron,  by  the  process  of  induction,  is  retained  only  so  long  as  the  mag- 
netising body  acts  upon  it.  Soon  after  the  two  bodies  are  separated 
the  bar  loses  all  magnetic  properties. 

When  a  bar  of  steel  is  placed  very  near  a  strong  magnet,  the  ac- 
tion of  the  magnet  commences  immediately  upon  the  end  of  the  bar 
nearest  to  it,  the  north  pole  for  example  communicating  south  polarity 
to  the  contiguous  extremity  of  the  bar.  According  to  our  previous 
experience,  we  should  expect  to  find  the  remote  end  of  the  bar  a 
north  pole ;  but  such  is  not  the  immediate  result ;  a  sensible  time  is 
required  before  the  north  polarity  is  fully  imparted  to  the  remote  ex- 
tremity. Indeed  if  the  bar  be  a  long  one,  it  sometimes  happens 
that  the  northern  polarity  never  reaches  the  farthest  end,  but  stops 
short  of  it  at  some  intermediate  point.  This  north  pole  is  succeeded 
by  a  second  south  pole,  that  by  another  north  pole,  and  thus  several 
alternations  between  the  two  poles  occur  before  reaching  the  end  of 
the  bar. 


243  MAGNETISM. 

452.  The  process  of  magnetizing  a  steel  bar  or  needle  is  accelera- 
ted by  any  cause  which  excites  a  tremulous  or  vibratory  motion 
among  the  particles  of  the  steel.  Striking  on  the  bar  with  a  ham- 
mer promotes  the  process  in  a  remarkable  degree,  especially  if  it  oc- 
casions a  ringing  sound,  which  indicates  that  the  particles  are  thrown 
into  a  vibratory  motion.  The  passage  of  an  electric  discharge  through 
a  steel  bar  under  the  influence  of  a  magnet,  produces  permanent 
magnetism.  Heat  also  greatly  facilitates  the  introduction  of  the 
magnetic  fluid  into  steel.  The  greatest  possible  degree  of  magnet- 
ism that  can  be  imparted  to  a  steel  bar  is  communicated  by  first 
heating  the  steel  to  redness,  and  while  it  is  under  the  influence  of  a 
strong  magnet,  quenching  it  suddenly  with  cold  water. 

A  magnet,  however,  loses  its  virtues  by  the  same  means  as,  du- 
ring the  process  of  induction,  were  used  to  promote  their  acquisition* 
Accordingly  any  mechanical  concussion,  or  rough  usage  impairs  or 
destroys  the  powers  of  a  magnet.  By  falling  on  a  hard  floor,  or  by 
being  struck  with  a  hammer  it  is  greatly  injured.  Heat  produces  a 
similar  effect.  A  boiling  heat  weakens  and  a  red  heat  totally  de- 
stroys the  power  of  a  needle.  On  the  other  hand,  cold  augments  the 
powers  of  the  magnet ;  indeed  they  improve  with  every  reduction  of 
temperature  hitherto  applied  to  them. 

453.  If  a  steel  bar,  rendered  magnetic  by  induction,  be  divided 
into  any  two  parts,  each  part  will  be  a  complete  magnet,  having  two 
opposite  poles. 

We  here  meet  with  a  remarkable  distinction  between  magnetic 
and  electric  induction.  When  a  body  electrified  by  induction,  is  di- 
vided into  two  equal  parts,  -the  individual  electricities  alone  remain 
in  each  part  respectively  ;  but  in  the  case  of  magnetic  induction,  al- 
though no  appearance  of  polarity  be  exhibited  except  at  the  two  ends, 
yet  wherever  a  fracture  is  made,  the  two  ends  separated  by  the 
fracture  immediately  exhibit  opposite  polarities,  each  being  of  an  op- 
posite name  to  that  of  the  original  pole  at  the  other  end  of  the  frag- 
ment. If  each  of  the  two  fragments  be  again  divided  into  any  num- 
ber of*parts,  each  of  these  parts  is  a  magnet  perfect  in  itself,  having 
two  opposite  poles. 

In  magnetism  therefore,  there  is  never  as  in  electricity,  any  trans- 
fer of  properties,  but  only  the  excitation  of  such  as  were  already  in- 


MAGNETIC    ATTRACTION.  249 

herent  in  the  body  acted  upon.  Magnetism  never  passes  out  of  one 
body  into  another ;  nor  can  we  ever  obtain  a  piece  of  iron  or  steel 
that  contains  exclusively  either  northern  or  southern  polarity. 

454.  The  force  of  attraction,  or  of  repulsion,  exerted  upon  each 
other  by  the  poles  of  two  magnets,  placed  at  different  distances,  varies 
inversely  as  the  square  of  the  distance. 

This  law  was  ascertained  by  means  of  a  very  delicate  appara- 
tus, in  a  manner  similar  to  that  adopted  in  investigating  the  law  of 
electrical  attraction.  The  same  law,  therefore,  which  governs  the 
attraction  of  gravitation,  likewise  controls  electrical  and  magnetic  at- 
tractions. It  is  the  most  extensive  law  of  the  physical  world.  Nor 
is  this  action  at  a  distance  prevented,  or  even  impaired,  by  the  inter- 
position of  other  bodies  not  themselves  magnetic. 

455.  The  magnetic  power  of  iron  resides  wholly  on  its  SURFACE, 
and  is  independent  of  the  mass. 

Thus,  a  hollow  globe  of  iron  of  a  given  surface,  will  have  the  same 
effect  on  the  needle  as  though  it  were  solid  throughout.  In  this  fact 
we  again  meet  with  a  striking  analogy  between  magnetism  and  elec- 
tricity, the  same  property  having  before  been  shown  to  belong  to  the 
electric  fluid.  This  is  one  of  the  most  recent  discoveries  in  magnet- 
ism, and  was  made  by  Professor  Barlow  of  the  Military  Academy  at 
Woolwich,  (Eng.)  to  whose  ingenious  and  assiduous  labors  are  due 
many  of  the  latest  and  most  important  investigations  in  this  science. 


CHAPTER  II. 

OF  THE  DIRECTIVE  PROPERTIES  OF  THE  MAGNET. 

456.  If  a  small  needle  be  placed  near  one  of  the  poles  of  a*  magnet 
with  its  center  in  the  axis  of  the  magnet,  it  will  take  a  direction  in  a 
line  with  that  axis. 

Thus,  let  S  N  be  a  large  mag-  Fig.  89. 

netic  bar  and  sn  a  small  needle     g 
placed  near  the  north  pole  of  the 
magnet  with  its  center  in  the  axis : 
it  will  be  seen  that  the  action  of  the 


250  MAGNETISM. 

pole  of  the  magnet  is  such  as  to  bring  the  needle  into  a  line  with  the 
magnet.  The  action  of  the  bar  upon  the  needle,  tending  to  give  it 
this  direction,  is  equal  to  the  sum  of  its  actions  upon  both  poles; 
while  the  attraction  of  the  bar  upon  the  whole  needle,  being  only  that 
by  which  the  attraction  for  s,  on  account  of  its  nearness,  exceeds  the 
repulsion  of  n,  must  be  less  than  the  directive  force. 

457.  If  the  needle  be  placed  at  right  angles  to  the  bar  with  one  of 
its  poles  directed  towards  the  center  of  the  bar,  it  will  take  a  direction 
parallel  to  the  bar. 

By  supposing  B  (Fig.  89.)  to  be  placed  as  indicated  in  the  above 
proposition,  it  will  be  seen,  that  the  actions  of  both  poles  of  the  magnet 
would  conspire  in  relation  to  each  pole  of  the  needle,  and  that  these 
forces  can  be  in  equilibrium  only  when  the  needle  is  parallel  with  the 
bar.  The  needle  in  this  situation  has  a  tendency  to  move  towards 
the  magnet,  because  the  attractions  being  exerted  on  the  nearer  and 
the  repulsions  on  the  remoter  poles,  the  sum  of  the  attractions  ex- 
ceeds that  of  the  repulsions. 

458.  Iron  filings  or  other  ferruginous  bodies,  which  are  free  to 
obey  the  action  of  a  magnetic  bar,  naturally  arrange  themselves,  in 
curve  lines,  from  one  pole  of  the  magnet  to  the  other. 

Thus,  if  we  place  a  sheet  of 

white  paper  on  a  magnetic  bar,         ,  ;,.  A-V-VV  ^o-.\\\  \ , 

laid  on  the  table,  and  sprinkle 
iron  filings  on  the  paper,  the 
filings  will  arrange  themselves 
in  curves  around  the  poles  of 
the  magnet. 

459.  The  magnetic  needle  when  freely  suspended  seldom  points  di- 
rectly to  the  pole  of  the  earth,  but  its  deviation  from  that  pole  is  call- 
ed the  DECLINATION,  or  the  VARIATION  of  the  needle. 

A  vertical  circle  drawn  through  the  line  in  which  the  needle  natu- 
rally places  itself,  is  called  the  magnetic  meridian.  A  plane  passing 
at  right  angles  to  the  magnetic  meridian,  through  the  center  of  the 
needle,  is  called  its  magnetic  equator.  A  line  drawn  on  the  surface 


DIRECTIVE    PROPERTIES    OF    THE    MAGNET.  251 

of  the  earth  passing  through  the  places  where  the  needle  points  di- 
rectly to  the  north  pole,  and  where  of  course  the  geographical  and 
magnetic  meridians  coincide,  is  called  the  line  of  no  variation. 

The  line  of  no  variation  encompasses  the  globe,  but  its  course  is 
subject  to  numerous  irregularities.  The  position  of  the  north  mag- 
netic pole,  where  it  may  be  supposed  to  commence,  is  not  exactly  as- 
certained, but  it  lies  in  the  northeastern  part  of  Hudson's  Bay.  Pro- 
ceeding southwards  it  crosses  the  United  States,  passing  a  little  to  the 
eastward  of  Barbadoes,  and  touching  the  northeastern  extremity  of 
South  America.  Thence  it  extends  across  the  Southern  Atlantic  to- 
wards the  south  pole,  where  navigators  have  not  been  able  to  trace  it. 

The  declination  of  the  needle  is  not  constant,  but  is  subject  to  a 
small  annual  change,  which  carries  it  to  a  certain  limit  on  one  side 
of  the  pole  of  the  earth,  when  it  becomes  stationary  for  a  time;  and 
then  returns  to  the  pole  and  proceeds  to  a  certain  limit  on  the  other 
side  of  it,  occupying  a  period  of  many  years  during  each  vibration. 

In  the  United  States,  the  variation  of  the  needle,  is  given  for  dif- 
ferent places  as  follows : — 

At  Salem,  Massachusetts,         1810,  6°  22'  35''.—Bowditch. 
New  Haven,  Connecticut,    1820,  4    25  25  . — Fisher. 
Albany,  New  York,  1825,  600  .-De  Witt. 

The  annual  variation  is  2'  49",  by  which  quantity  the  needle  ap- 
proaches the  pole. 

The  variation  of  the  needle  however  is  not  the  same  at  the  same 
time  in  all  parts  of  the  earth,  but  every  place  has  its  particular  decli- 
nation. For  instance,  if  we  sail  from  the  Straits  of  Gibraltar  to  the 
West  Indies,  in  proportion  as  we  recede  from  Europe  and  approach 
America,  the  compass  will  point  nearer  and  nearer  due  north;  and 
when  we  reach  a  certain  part  of  the  Gulf  of  Mexico  it  will  point  ex- 
actly north.  But  if  we  sail  from  Great  Britain  to  the  southern  coast 
of  Greenland,  we  shall  find  the  needle  deviate  farther  and  farther 
form  the  north,  as  we  approach  Greenland,  where  the  deviation  will 
not  be  less  than  45°  or  50°.  In  some  parts  of  Baffin's  Bay  the 
needle  points  nearly  due  west. 

460.  Beside  the  annual  variation,  the  magnetic  needle  is  subject  to 
daily  changes  called  the  DIURNAL  VARIATION. 


252  MAGNETISM. 

The  deviation  of  the  horizontal  needle  from  its  mean  position  is 
easterly  during  the  forenoon,  and  arrives  at  its  maximum  about  eight 
o'clock.  Thence  it  returns  rapidly  to  its  mean  position,  which  it 
reaches  between  nine  and  ten  o'clock,  and  then  its  variation  becomes 
westerly;  at  first  increasing  rapidly,  so  as  to  reach  its  maximum  at 
about  one  o'clock  in  the  afternoon,  and  then  slowly  receding  during 
the  rest  of  the  day,  and  arriving  at  its  mean  position  about  ten 
o'clock  at  night. 

461.  Jl  needle  first  balanced  horizontally  on  its  center  of  gravity 
and  then  magnetised,  no  longer  retains  its  level,  but  its  north  pole 
spontaneously  takes  a  direction  to  a  point  below  the  horizon  called  the 

DIP    OF    THE  NEEDLE. 

The  Dipping  Needle,  is  represented  Fie.  91. 

in  Fig.  91.  When  used  it  is  to  be  pla- 
ced in  the  magnetic  meridian,  and  to  ren- 
der the  stand  which  supports  it,  perfectly 
level,  by  means  of  the  adjusting  screws 
attached. 

The  dip  of  the  needle  is  very  different 
in   different  parts  of  the  globe,  being  in 

genera]  least  in  the  equatorial  and  great-     "  ft  w 

est  in  the  polar  regions.  At  certain  places  on  the  globe  the  needle 
has  no  dip,  that  is,  becomes  perfectly  horizontal,'  and  a  line  uniting 
all  such  places  is  called  the  magnetic  equator  of  the  earth.  Again, 
in  the  Polar  Regions,  the  dipping  needle  sometimes  becomes  nearly 
perpendicular  to  the  horizon.  In  the  middle  latitudes,  .the  dip  is 
greater  or  less  but  does  not  correspond  exactly  to  the  latitudes. 

462.  The  force  exerted  by  the  magnetism  of  the  earth  varies  in  dif- 
ferent places :  its  comparative  estimate  for  any  given  place,  is  called 
the  MAGNETIC  INTENSITY /or  that  place. 

As  in  the  case  of  the  pendulum  in  its  relation  to  the  force  of  grav- 
ity, the  magnetic  intensity  may  be  measured  by  the  number  of  oscil- 
lations, ^which  a  needle  drawn  a  given  number  of  degrees  from  its 
point  of  rest,  performs  in  a  certain  time,  as  a  minute  for  example, 
the  force  being  as  the  square  of  the  number  of  oscillations.  In  gen- 
eral it  is  well  ascertained  that  the  magnetic  intensity  is  least  in  the 


DIRECTIVE    PROPERTIES    OF    THE    MAGNET.  253 

equatorial  regions  and  increases,  as  we  advance  towards  the  poles. 
It  is  probably  at  its  maximum  at  the  magnetic  poles.  By  ascertain- 
ing from  actual  observation,  a  number  of  different  places  on  the  sur- 
face of  the  earth  where  the  magnetic  intensities  are  equal,  and  con- 
necting them  by  a  line,  it  appears  that  they  arrange  themselves  in  a 
curve  around  the  magnetic  pole.  These  lines  are  called  isodynamic 
curves.  Extensive  journeys,  have  been  undertaken  by  Humboldt, 
Sabine,  Hansteen  and  others,  to  ascertain  the  point  on  the  surface  of 
the  earth  where  the  magnetic  intensities  are  equal,  for  the  purposes 
of  describing  these  curves.  The  earlier  results  indicated  the  posi- 
tion of  the  magnetic  pole  to  be  in  the  northeastern  part  of  Hudson's 
Bay,  lat.  60°  N.  Ion.  80°  W.  ;*  but  the  directions  of  these  curves 
presented  such  anomalies  as  to  suggest  the  idea  of  a  second  magnet- 
ic pole  in  the  opposite  hemisphere.  With  a  view  of  ascertaining  this 
point,  Professor  Hansteen  of  Christiana  several  years  since,  under- 
took a  journey  into  Siberia,  at  the  expense  of  the  King  of  Sweden, 
and  has  fully  confirmed  the  fact,  that  there  exists  a  second  magnetic 
pole  to  the  north  of  Siberia,  around  which  the  isodynamic  curves  ar- 
range themselves  in  regular  order.  From  experiments  made  in  deep 
mines  and  in  the  upper  regions  of  the  atmosphere  by  aeronauts,  it 
appears  that  in  both  these  situations,  the  magnetic  intensity  is  the 
same  as  at  the  corresponding  places  on  the  surface  of  the  earth. 

463.  The  effects  produced  by  the  earth  on  a  magnetic  needle,  cor- 
respond to  those  produced  on  it  by  a  powerful  m  agnet,  and  hence  the 
earth  itself  may  be  considered  as  such  a  magnet. 

The  magnetism  of  the  earth  has  been  supposed  by  some  to  result, 
from  a  great  magnet  lying  in  the  central  parts  of  the  earth ;  by 
others,  to  be  nothing  more  than  the  resultant  of  all  the  smaller  mag- 
netic forces  scattered  through  various  parts  of  the  terrestial  sphere ; 
and  by  others  to  be  excited  on  the  surface  of  the  earth  by  the  action 
of  the  solar  rays. 

The  supposition  of  a  great  magnet  in  the  interior  of  the  earth,  to 
which  all  the  phenomena  of  terrestrial  magnetism  are  to  be  ascribed 


*  Capt.  Parry  fixes  the  place  of  the  magnetic  pole  in  102°  W.  lon- 
and  73°  N.  lat. 

*?f* 


254  MAGNETISM. 

is  the  earliest  hypothesis,  and  is  adequate  to  explain  most  of  the  facts 
of  the  science.  But  such  a  supposition  is  inconsistent  with  the  re- 
cent discovery  of  two  north  poles  implying  the  existence  of  four 
magnetic  poles  of  the  earth.  The  opinion  of  Biot,  that  terrestrial 
magnetism  is  only  the  aggregate  or  resultant,  of  all  the  individual 
magnetic  forces  residing  in  different  parts  of  the  earth,  appears  to  be 
no  improbable  supposition,  and  accords  well  with  the  general  doctrine 
of  the  composition  of  forces. 

464.  In  the  year  1813,  Dr.  Morichini,  of  Rome,  announced  that 
the  violet  rays  of  the  solar  spectrum  have  the  property  of  rendering 
iron  magnetic.     In  1825,  these  experiments  were  repeated  and  ex- 
tended by  Mrs.  Sommerville,  and  resulted  in  proving  that  the  magne- 
tizing power  is  not  confined  to  the  violet  rays,  but  extends  to  the  in- 
digo, blue,  and  green  rays.     The  probable  conclusion  is,  that  a  class 
of  rays  emanate  from  the  sun  which  have  the  property  of  producing 
magnetism,   and  are  distinct  from  those  which  afford  light  and  heat, 
and  produce  chemical  changes.     Hence  in  the  solar  beam  there  are 
at  least  four  distinct  kinds  of  rays,  denominated,  respectively,  colorific, 
calorific,  chemical,  and  magnetising  rays. 

465.  Electricity  and  magnetism  are,  in  some  of  their  properties, 
remarkably  alike,  but  in  others  strikingly  dissimilar. 

Several  of  these  analogies  have  been  already  incidentally  mention- 
ed ;  but  it  will  be  useful  to  the  student  to  consider  them  in  connec- 
tion. Electricity  and  magnetism  agree  in  the  following  particulars : 
(1.)  Each  consist  of  two  species,  the  vitreous  and  resinous  electri- 
cities, and  the  austral  and  boreal  magnetisms.  (2.)  In  both  cases, 
those  of  the  same  name  repel,  and  those  of  opposite  names  attract 
ea*ch  other.  (3.)  The  laws  of  induction  in  both  are  very  analogous. 
(4.)  The  force,  in  each,  varies  inversely  as  the  square  of  the  dis- 
tance. (5.)  The  power,  in  both  cases,  resides  at  the  surface  of  bod- 
ies, and  is  independent  of  their  mass. 

But  electricity  and  magnetism  are  as  remarkably  unlike  in  the  fol- 
lowing, particulars.  (1.)  Electricity  is  capable  of  being  excited  in 
all  bodies  and  of  being  imparted  to  all :  magnetism  resides  almost 
exclusively  in  iron  in  its  different  forms,  and,  with  a  few  exceptions, 
cannot  be  excited  in  any  other  than  ferruginous  bodies.  (2.)  Elec- 


DIRECTIVE    PROPERTIES    OP    THE    MAGNET.  255 

tricity  may  be  transferred  from  one  body  to  another :  magnetism  is 
incapable  of  such  transference ;  magnets  communicate  their  proper- 
ties merely  by  induction,  a  process  in  which  no  portion  of  the  fluid 
is  withdrawn  from  the  magnetizing  body.  (3.)  When  a  body  of  elon- 
gated figure  is  electrified  by  induction,  on  being  divided  near  the 
middle,  the  two  parts  possess  respectively  the  kind  of  electricity  only 
which  each  had  before  the  separation ;  but  when  a  bar  of  steel  or  a 
needle  magnetized  by  induction,  is  broken  into  any  number  of  parts, 
each  part  has  both  polarities  and  becomes  a  perfect  magnet.  (4.)  The 
directive  properties  and  the  various  consequences  that  result  from  it, 
the  declination,  annual  and  diurnal  variations,  the  dip,  and  the  differ- 
ent intensities  in  different  parts  of  the  earth,  are  all  peculiar  to  the 
magnet  and  do  not  appertain  to  electrified  bodies. 

Method  of  making  Artificial  Magnets. 

466.  If  the  learner  has  made  himself  acquainted  with  the  princi- 
ples expounded  in  the  preceding  propostions,  he  will  be  qualified  to 
proceed,  with  interest  and  intelligence,  to  an  explanation  of  the  lead- 
ing methods  practised  in  the  manufacture  of  artificial  magnets.  These 
methods  also,  by  involving  a  practical  application  of  those  principles, 
will  serve  to  impress  them  on  the  memory  and  to  render  the  knowl- 
edge of  them  familiar. 

It  will  be  recollected  that  magnets  are  made  from  other  magnets ; 
that  this  is  done  not  by  any  transference  of  a  portion  of  the  power  of 
the  magnetizing  body,  but  by  the  development  of  the  powers  nat- 
urally residing  in  the  body  to  be  magnetized ;  that  this  development 
is  effected  wholly  on  the  principle  of  induction ;  that  the  original 
magnet  gains  instead  of  losing  by  its  action  on  other  bodies ;  that 
this  power  may  be  induced  on  iron  by  the  agency  of  an  artificial 
magnet,  or  of  the  loadstone,  or  of  the  earth  which  is  itself  a  weak 
magnet,  and  acts  upon  the  same  principles  as  any  other  magnet.  It 
must  also  be  kept  clearly  in  mind,  that  soft  iron  or  steel  readily  ac- 
quires and  as  readily  loses  the  magnetism  induced  upon  it,  and  that 
hardened  iron  or  steel  receives  it  slowly  and  with  much  difficulty  but 
retains  it  permanently.  As  the  earth  itself  may  be  supposed  to  have 
been  the  original  source  of  magnetism  in  all  other  bodies  in  which  it 
is  found,  there  are  methods  of  magnetizing  from  the  earth  without 
the  aid  of  either  a  loadstone  or  an  artificial  magnet. 

:  '*«* 


256  MAGNETISM. 

467.  Jl  needle  may  be  magnetized  by  simply  suffering  it  to  remain 
in  contact  with  the  pole  of  a  strong  magnet ;  or  better  between  the 
opposite  poles  of  two  magnets. 

The  effect  produced  by  two  magnets  is  much  more  than  double 
that  of  one  magnet,  as  may  be  inferred  from  article  448.  But  if 
the  needle  be  of  considerable  length,  several  intermediate  sets  of 
poles  are  sometimes  developed,  as  will  be  seen  by  applying  iron 
filings.  It  adds  much  to  the  power  of  the  two  magnetic  bars  between 
which  the  needle  is  placed,  if  to  the  extremity  of  the  bar  most  re- 
mote from  the  needle,  a  mass  of  soft  iron  is  placed.  The  iron  in 
this  case,  acts  and  reacts  by  induction  ;  and  hence  whenever  magnets 
are  not  in  use,  they  require  to  be  connected  with  iron  to  prevent  the 
loss  of  their  powers.  Pieces  of  soft  iron  thus  connected  with  mag- 
nets for  the  purpose  of  augmenting  their  power  by  induction,  .are  call- 
ed armatures.  Thus  A  is  the  armature  of  the  horse  shoe  magnet 
represented  in  figure  93. 

468.  But  it  must  be  recollected  that  the  two  species  of  magnet- 
ism are  not,  like  those  of  electricity,  separated  to  a  distance  from 
each  other,  so  that  one  kind  may  be  wholly  collected  at  one  end  of 
the  bar  and  the  other  kind  at  the  other  end ;  but  that  the  two  are 
separated  only  at  a  minute  distance  remaining  in  the  immediate  vi- 
cinity of  each  other  throughout  the  whole  length  of  the  bar.  Hence, 
in  order  to  give  the  magnetizing  pole  its  full  effect,  it  becomes  neces- 
sary to  apply  it  successively  to  every  part  of  the  bar  from  one  end  to 
the  other. 

A  more  effectual  method  of  magnetizing  a  needle  is  the  following  : 
Place  two  magnetizing  bars  A,  B,  par- 
allel to  each  other,  with  their  dissimi- 
lar poles  adjacent;  unite  the  poles  at 
one  end  by  a  piece  of  soft  iron  R,  and 
apply  the  poles  at  the  other  end  to 
the  needle,  as  is  represented  in  fig.  92.  Upon  this  principle,  that  is, 
the  increased  energy  with  which  the  two  poles  act  together,  is  formed 
what  is  called  the  horse  shoe  magnet,  which  derives  its  name  from 
its  peculiar  figure,  (fig.  93.)  Bars  of  Fig.  93. 

this  form  are  converted  into  magnets 
upon  the  same  principles  as  straight   A 
bars,  the  magnetizing  bar,  being  made 


THE   COMPASS.  257 

to  follow  the  curvature  always  in  the  same  direction.  A  very  effi- 
cacious mode  of  making  horse  shoe  magnets  is  thus  described  by 
Professor  Barlow.  Two  horse  shoe  bars  may  be  united  at  their 
ends,  in  such  a  manner  that  the  poles  which  are  to  be  of  opposite 
names  shall  be  in  contact.  They  are  then  to  be  rubbed  with  anoth- 
er strong  horse  shoe  magnet,  placing  the  latter  so  that  its  north  pole 
is  next  to  the  south  pole  of  one  of  the  new  magnets,  and  conse- 
quently its  south  pole  next  to  the  north  pole  of  the  same ;  carrying 
the  movable  magnet  round  and  round  always  in  the  same  direction. 
This  is  esteemed  one  of  the  most  eligible  modes  of  making  powerful 
magnets. 

The  horse  shoe  magnet  is  itself  very  convenient  for  imparting  mag- 
netism to  other  bodies.  Place  the  poles  near  the  center  of  the  nee- 
dle ;  move  them  along  its  surface  backwards  and  forwards,  taking 
care  to  pass  over  each  half  of  it  an  equal  number  of  times ;  repeat 
the  same  operation  on  the  other  side ;  and  the  needle  will  become 
speedily  and  effectually  magnetized. 

469.  The  best  mode  of  making  magnetic  needles  in  general,  is 
expressed  in  the  following  rule,  given,  as  the  result  of  very  exten- 
sive and  accurate  experiments  by  Capt.  Kater. 

Place  the  needle  in  the  magnetic  meridian  ;  join  the  opposite  poles 
of  a  pair  of  bar  magnets,  (the  magnets  being  in  the  same  line)  and 
lay  the  magnets  so  joined,  flat  upon  the  needle,  with  their  poles  upon 
its  center ;  then  having  elevated  the  distant  extremities  of  the  mag- 
nets, so  that  they  may  form  an  angle  of  about  two  or  three  degrees 
with  the  needle,  draw  them  from  the  center  of  the  needle  to  the  ex- 
tremities, carefully  preserving  the  same  inclination;  and  having  join- 
ed the  poles  of  the  magnets  at  a  distance  from  the  needle,  repeat  the 
operation  ten  or  twelve  times  on  each  surface. 

The  Compass. 

470.  The  Compass,  (the  importance  of  which  to  mankind,  has 
attached  to  the  subject  of  magnetism  its  principal  value,)  is  of  many 
different  forms,  but  the  chief  varieties  are  the  Land  compass,  the 
Mariner's  compass,  the  Azimuth  compass,  and  the  Variation-  com- 

33 


258  MAGNETISM. 

pass.     The  needle,  in  all  these  varieties,  is  usually  a  thin  flat  plate 
of  steel,  tapering  at  the  extremities ;  but,  a  more  eligible  form  has 
been   proposed   by  Capt.   Kater, 
consisting  of  four  narrow  strips  of  Fl8-  94< 

steel,  united  in  the  form  of  a  hol- 
low rhombus,  (Fig.  94.)  It  is 
found  advantageous  to  concen- 
trate the  powers  of  the  needle  as 

much  as  possible  in  the  two  extremities,  and  to  avoid  all  inequalities, 
arising  from  intermediate  poles,  or  from  a  difference  of  strength  in 
different  parts.  The  needle  is  secured  at  the  point  of  suspension, 
and  furnished  with  a  conical  cap  of  brass  which  rests  on  a  perpen- 
dicular pin ;  and  still  farther  to  diminish  friction,  the  point  which 
rests  on  the  extremity  of  the  pin,  is  made  of  agate,  one  of  the  hard- 
est mineral  substances.  Since,  if  the  needle  is  magnetized  after 
having  been  balanced  on  its  center  of  gravity,  it  would  no  longer 
remain  horizontal,  the  equipoise  is  restored  by  attaching  a  small 
weight  to  the  elevated  side. 

471.  The  compass,  in  its  simplest  form,  consists  of  a  needle  like 
the  foregoing  enclosed  in  a  suitable  box  covered  with  glass.     This  is 
all  that  is  essential  when  it  is  required  merely  to  know  the  direction 
of  the  meridian,  or  the  north  and  south  points.     But,  for  most  purpo- 
ses, the  compass  is  furnished  with  a  graduated  circular  card,  divided 
into  degrees  and  minutes ;  and  in  the  mariner's  compass  the  card  is 
also  divided  into  thirty  two  equal  parts  called  rhumbs.     The  card 
thus  divided  is  fastened  to  the  needle  itself,  and  turns  with  it. 

i 

472.  Thin,  slender  needles  have  the  greatest  directive  powers, 
and  are  most  sensible,  since  they  undergo  less  friction  than  those  which 
are  heavier,  but  due  regard  to  strength  requires  them  to  be  made  of 
a  certain  degree  of  thickness ;  an  increase  of  length  is  attended  with 
an  increase  of  directive  power ;  but  when  the  thickness  remains  the 
same,  the  weight,  and  consequently  the  friction,  increases  in  the  very 
same  ^catio ;  no  advantage,  therefore,  as  to  directive  power,  can  be 
obtained  by  any  increase  of  length.     Moreover,  needles  which  ex- 
ceed a  very  moderate  length,  are  liable  to  have  several  sets  of  poles, 
a  circumstance  which  is  attended  with  a  great  diminution  of  directive 


THE    COMPASS. 


259 


force.     On  this  account,  short  needles,  made  exceedingly  hard,  are 
generally  preferable. 

473.  The  great  importance  of  the  mariner's  compass,  has  made 
its  construction  an  object  of  much  attention,  and  the  best  artists  have 
tried  their  skill  upon  it.  The  compass  is  suspended  in  its  box  in  such 
a  manner  as  to  remain  in  a  horizontal  position  notwithstanding  all  the 
motions  of  the  ship.  This  is  effected  by  means  of  gimbals.  This 
contrivance  consists  of  a  hoop,  usually  of  brass,  (Fig.  95.)  fastened 

Fig.  95. 


horizontally  to  the  box  by  two  pivots  placed  opposite  to  each  other, 
and  constituting  the  axis  on  which  the  hoop  turns  up  and  down.  At 
an  equal  distance  from  the  pivots  on  each  side,  that  is,  at  the  distance 
of  90°  from  each  pivot,  two  other  pivots  are  attached  to  the  ring  at 
right  angles  to  the  former,  on  which  the  inner  box  that  contains  the 
card  is  hung.  Of  course  when  it  turns  on  these  pivots,  its  motion  is 
at  right  angles  with  that  of  the  hoop.  Therefore,  all  the  motions 
of  which  the  compass  box  is  capable,  are  performed  around  two 
axes  which  intersect  each  other  at  right  angles ;  consequently,  the 
point  of  intersection,  being  in  both  axes,  will  not  move  at  all.  But 
the  needle  and  the  attached  card  rest  upon  this  point,  and  are  con- 


260  MAGNETISM. 

nected  with  the  compass  box  in  no  other  point.     Hence  they  remain 
constantly  horizontal  in  every  position  of  the  box. 

The  Azimuth  compass*  differs  from  the  common  mariner's  com- 
pass only  in  having  sights  attached,  by  which  the  bearing  of  any  ob- 
ject with  the  meridian  may  be  ascertained.  The  Surveyor's  corn- 
is  a  variety  of  the  azimuth  compass. 


*  Azimuth,  as  applied  to  a  star  or  any  celestial  object,  is  an  arc  of 
the  horizon  intercepted  between  the  meridian  and  a  vertical  circle 
passing  through  the  object. 


261 


PART    VI. OPTICS. 


PRELIMINARY  DEFINITIONS  AND  OBSERVATIONS. 

474.  OPTICS  is  that  branch  of  Natural  Philosophy  which  treats 
of  Light  and  Vision. 

More  particularly,  it  is  the  object  of  this  science  to  investigate  the 
nature  of  the  agent  on  which  the  phenomena  of  vision  depend ;  to 
treat  of  the  motions  of  light,  in  respect  to  its  direction,  its  velocity, 
and  its  reflexion  from  the  surfaces  of  bodies,  to  trace  its  change  of 
direction,  and  the  various  other  modifications  it  undergoes  by  passing 
through  different  transparent  media ;  to  explain  the  phenomena  of 
nature  which  depend  upon  the  properties  of  light,  embracing  the  doc- 
trine of  color;  to  trace  the  relation  between  light  and  the  structure 
of  the  eye,  comprehending  the  subject  of  vision;  and  finally,  to  de- 
scribe the  various  instruments  to  which  a  knowledge  of  the  principles 
of  Optics  has  given  birth,  disclosing  many  new  and  wonderful  prop- 
erties of  light,  and  extending  the  range  of  human  vision,  on  the  one 
hand,  to  myriads  of  objects  too  minute,  and  on  the  other,  to  number- 
less worlds  too  remote,  to  be  seen  by  the  unassisted  eye. 

475.  Luminous  bodies  are  naturally  of  two  kinds,  such  as  shine 
by  their  own  light,  as  a  lamp  or  the  sun,  and  such  as  shine  by  bor- 
rowed light,  as  the  moon,  and  most  of  the  visible  objects  in  nature. 

A  ray  is  a  line  of  light ;  or  it  is  the  line  which  may  be  conceived 
to  be  described  by  a  particle  of  light.  In  a  more  general  sense,  the 
term  is  applied  to  denote  the  smallest  portion  of  light  which  can  be 
separately  subjected  to  experiment.  A  beam  is  a  collection  of  par- 
allel rays.  A  pencil  is  a  collection  of  converging  or  diverging  rays. 
A  medium  is  any  space  through  which  light  passes.  When  a  space 
is  a  perfect  void,  so  as  to  offer  no  obstruction  to  the  passage  of  light, 
it  is  said  to  be  a  free  medium ;  when  the  space  intercepts  a  portion 
only  of  the  light,  it  constitutes  a  transparent  medium.  Transparency, 
however,  may  exist  in  different  degrees.  When  the  medium  itself  is 


262  OPTICS. 

invisible,  as  portions  of  air,  it  is  said  to  be  perfectly  transparent ; 
when  the  medium  is  visible,  but  objects  are  seen  distinctly  through 
it,  as  in  the  clearest  specimens  of  glass  and  crystals,  it  is  said  to  be, 
simply,  transparent;  when  objects  are  indistinctly  seen  through  it,  it 
is  semi-transparent ;  and  when  a  mere  glimmering  of  light  passes 
through,  without  representing  the  figure  of  objects,  it  is  translucent. 
Bodies  that  transmit  no  light  are  said  to  be  opake. 

476.  Rays  of  light,  while  they  continue  in  the  same  uniform  me- 
dium, proceed  in  straight  lines. 

For  objects  cannot  be  seen  through  bent  tubes ;  the  shadows  of 
bodies  are  terminated  by  straight  lines;  and  all  the  conclusions  drawn 
from  this  supposition,  are  found  by  experience  to  be  true.  If  two 
bodies  with  plane  surfaces,  as  two  disks  of  metal,  be  held  between 
the  eye  and  some  luminous  point,  as  a  star,  on  bringing  the  two  planes 
gradually  towards  each  other,  the  star  may  be  seen  through  the  in- 
tervening space  until  the  planes  come  completely  into  contact ;  but 
if  one  of  the  surfaces  is  convex  and  the  other  concave,  the  light  is 
intercepted  before  the  surfaces  have  met.  In  consequence  of  the 
rectilinear  motion  of  light,  it  forms  angles,  triangles,  cylinders,  cones, 
&c.,  and  thus  its  affections  fall  within  the  province  of  geometry,  the 
principles  of  which  are  applied  with  great  effect  to  the  development 
of  the  properties  and  laws  of  light,  after  a  few  fundamental  properties 
are  established  by  experiment.  From  every  point  in  a  luminous  ob- 
ject, an  inconceivable  number  of  rays  of  light  emanate  in  every  di- 
rection when  not  prevented  by  obstacles  that  intercept  it.  Thus, 
from  every  point  in  the  flame  of  a  candle,  as  seen  by  night,  light 
diffuses  itself,  pervading  an  immense  sphere,  and  filling  every  part  of 
the  space  so  perfectly,  that  not  the  minutest  point  can  be  found  des- 
titute of  some  portion  of  its  rays.  Any  luminous  body  of  this  kind 
is  called  a  radiant.  The  pencil  of  light  which  proceeds  from  a  ra- 
diant, is  a  cone,  the  sections  of  which  made  by  any  plane  corres- 
pond to  the  figures  called  conic  sections.  If  any  portion  of  the 
pencil  be  intercepted  by  a  rectilateral  figure,  that  portion  constitutes 
a  pyramid  of  which  the  figure  is  the  base  and  the  luminous  point  it- 
self is  the  vertex. 

477.  Light  has  a  progressive  motion  of  about  one  hundred  and 
ninety  two  thousand  Jive  hundred  miles  per  second. 


PRELIMINARY  DEFINITIONS  AND  OBSERVATIONS.      363 

The  estimation  of  the  velocity  of  light,  (which  may  be  classed 
among  the  greatest  achievements  of  the  human  mind,)  has  been  ef- 
fected in  two  different  ways.  The  first  method  is  by  means  of  the 
eclipses  of  Jupiter's  satellites.  To  render  this  mode  intelligible  to 
those  who  have  not  studied  astronomy,  it  may  be  premised,  that  the 
planet  Jupiter  is  attended  by  four  moons  which  revolve  about  their 
primary  as  our  moon  revolves  about  the  earth.  These  small  bodies 
are  observed,  by  the  telescope,  to  undergo  frequent  eclipses  by  falling 
into  the  shadow  which  the  planet  casts  in  a  direction  opposite  to  the 
sun.  The  exact  moment  when  the  satellite  passes  into  the  shadow, 
or  comes  out  of  it,  as  seen  by  a  spectator  on  the  earth,  is  calculated 
by  astronomers.  But  sometimes  the  earth  and  Jupiter  are  on  the 
same  side,  and  sometimes  on  opposite  sides  of  the  sun  ;  consequent- 
ly, the  earth  is,  in  the  former  case,  the  whole  diameter  of  its  orbit, 
or  about  one  hundred  and  ninety  millions  of  miles  nearer  to  Jupiter 
than  in  the  latter.  Now  it  is  found  by  observation,  that  an  eclipse  of 
one  of  the  satellites  is  seen  about  sixteen  minutes  and  a  half  sooner 
when  the  earth  is  nearest  to  Jupiter,  than  when  it  is  most  remote  from 
it,  and  consequently,  the  light  must  occupy  this  time  in  passing  through 
the  diameter  of  the  earth's  orbit,  and  must  therefore  travel  at  the  rate 
of  about  one  hundred  and  ninety  two  thousand  miles  per  second.* 
Another  method  of  estimating  the  velocity  of  light,  wholly  independent 
of  the  preceding,  is  derived  from  what  is  called  the  aberration  of 
the  fixed  stars.  The  full  explanation  of  this  method  must  be  refer- 
red to  astronomy ;  but  it  may  be  understood,  in  general,  that  the 
apparent  place  of  a  fixed  star  is  altered  from  the  effect  of  the  mo- 
tion of  its  light  combined  with  the  motion  of  the  earth  in  its  orbit. 
It  will  be  remarked,  that  the  place  of  a  luminous  object  is  determin- 
ed by  the  direction  in  which  its  light  meets  the  eye.  But  in  the 
case  of  light  coming  from  the  stars,  the  direction  is  altered  in  con- 
sequence of  the  motion  of  the  earth  in  its  orbit,  being  intermediate 
between  the  actual  directions  of  the  earth  and  the  light  of  the  star ; 
and  the  velocity  of  the  earth  in  its  orbit  being  known,  that  of  light 
may  be  computed  from  the  proportional  part  of  the  effect  produced 
by  it  in  causing  the  aberration.  The  velocity  of  light,  as  deduced 

190000000 


264  OPTICS. 

from  this  method,  comes^out  very  nearly  the  same  as  by  the  other. 
Hence  it  is  inferred  that  the  velocity  of  light  is  uniform. 

478.  The  intensity  of  light,  at  different  distances  from  the  radi- 
ant, varies  inversely  as  the  square  of  the  distance. 

Thus  if  we  carry  a  given  surface,  as  a  leaf  of  paper,  to  different 
distances  from  a  candle,  at  the  distance  of  six  feet  the  surface  will 
receive  only  J  as  much  light  as  at  the  distance  of  three  feet ;  at  12 
feet,  or  four  times  as  far  as  at  first,  the  light  will  be  only  TV  as  in- 
tense. Although  the  intensity  of  light  decreases  rapidly  as  we  re- 
cede from  the  radiant,  yet  the  Irightness  of  the  object  suffers  little 
diminution  by  increase  of  distance.-  A  candle  appears  nearly  as 
bright  at  the  distance  of  a  mile  as  when  close  to  the  eye. 

479.  Light,  when  it  impinges  on  smooth  surfaces,  is  reflected  back 
into  the  same  medium,   and  when  it  passes  out  of  one  medium  into 
another,  it  is  bent  out  of  its  former  course,  or  refracted.     The  laws 
of  reflexion  and  refraction  constitute,  severally,  important  depart- 
ments of  the  science  of  Optics,  and  to  these  our  attention  will  now 
be  directed. 


CHAPTER  I. 

OF  THE  REFLEXION  OF  LIGHT. 

480.  Light  is  said  to  be  reflected  when,  on  impinging  upon  any 
surface,  it  is  turned  back  into  the  same  medium. 

Instruments  employed  as  reflectors  are  divided  into  mirrors  and 
speculums.  The  name  mirror  is  applied  to  reflectors  made  of  glass 
and  coated  with  quicksilver,  as  common  looking  glasses :  the  word 
speculum  is  applied  to  a  metallic  reflector,  such  as  those  made  of 
silver,  steel,  tin,  or  a  peculiar  alloy  called  speculum  metaJ.  As  the 
light  which  falls  on  glass  mirrors,  is  intercepted  by  the  glass  before 
it  is  reflected  from  the  quicksilvered  surface,  a  speculum,  or  a  re- 
flector of  polished  metal,  is  that  supposed  to  be  employed  in  optic- 
al experiments,  unless  the  contrary  is  specified.  Such  a  surface, 


REFLEXION    OF    LIGHT.  265 

indeed,  is  to  be  understood  where  the  word  mirror  is  used  without 
distinction. 

The  surface  of  the  mirror  or  speculum  may  be  either  plane,  con- 
cave, or  convex,  and  the  reflector  is  denominated  accordingly. 

A  ray  of  light  before  reflexion  is  called  the  incident  ray.  The 
angle  made  by  an  incident  ray,  at  the  surface  of  the  reflector,  with 
a  perpendicular  to  that  surface,  is  called  the  angle  of  incidence :  the 
angle  made  by  the  reflected  ray  with  the  same  perpendicular  is  call- 
ed the  angle  of  reflexion.  Thus,  in 
Fig.  96,  if  MN  represents  the  re- 
flecting surface,  DC  a  perpendicular 
to  it  at  the  point  C,  AC  the  inci- 
dent, and  BC  the  reflected  ray ;  then 
ACD  will  be  the  angle  of  incidence, 
and  BCD  the  angle  of  reflexion.  -^  ^  Nl 

481.  Experiments  on  light  are  usually  conducted  in  a  room  which 
can  be  made  dark  with  close  shutters,  one  of  which  is  perforated 
with  a  circular  hole,  a  few  inches  in  diameter,  for  admitting  a  beam  of 
light.     This  opening  is  rendered  smaller  to  any  required  degree  by 
covering  it  with  a  piece  of  board  or  metallic  sheet,  having  a  smaller 
aperture.     And,  as  the  sun  may  not  shine  directly  into  the  shutter  at 
the  time  required,  a  mirror  is  sometimes  attached  to  the  outside  of 
the  shutter,  so-contrived  that,  by  means  of  adjusting  screws,  it  may 
be  made  to  turn  the  rays  of  the  sun  into  the  opening,  and  to  give 
them  a  horizontal  or  any  other  required   direction.     The  course  of 
the  rays  is  rendered  palpable  to  the  eye,  by  the  illuminated  particles 
of  dust  that  are  floating  in  the  air. 

482.  The  angles  of  incidence  and  reflexion  are  in  the  same  plane, 
and  are  equal  to  each  other. 

Let  a  ray  of  light  AC  (Fig.  96.)  admitted  into  a  dark  chamber  as 
above,  be  incident  upon  a  horizontal  speculum  MN  at  the  point  C, 
to  which  the  line  CD  is  perpendicular,  and  let  CB  be  the  reflected 
ray.  Then  if  the  plane  surface  of  a  board  or  a  metallic  plate,  be 
made  to  coincide  with  the  incident  ray  and  the  perpendicular,  it  will 
be  found  to  coincide  also  with  the  reflected  ray,  showing  that  the 
three  rays  are  in  the  same  plane.  Again,  if,  from  the  point  C,  with 

34 


266 


OPTICS. 


the  radius  CA,  a  circle  be  described,  on  measuring  the  arcs  subten- 
ded by  the  angles  of  incidence  and  reflexion,  they  will  be  found  to 
be  exactly  equal  to  each  other.  The  angles  of  incidence  and  reflex- 
ion are  also  equal  when  the  reflexion  takes  place  from  a  concave  or 
convex  surface ;  for  the  reflexion  being  from  a  point,  the  curve  and 
tangent  plane  at  that  point  coincide,  and  have  both  the  same  perpen- 
dicular, namely  the  radius  of  the  curve. 

Reflexion  of  Light  from  Plane  Mirrors. 

483.  When  rays  of  light  are  reflected  from  a  plane  surface,  the 
reflected  rays  have  the  same  inclination  to  one  another  as  their  cor- 
responding incident  rays. 

When  parallel  rays  as  AB,  CD,  (Fig.  97.)  fall  upon  a  plane  mir- 
ror, as  RS,  the  reflected  rays  BG,  DH,  are  also  parallel. 


Fig.  97. 


Moreover  when  the  rays  diverge  before  reflexion  (Fig.  98.) 
as  RA,  RB,  they  will  diverge  just  as  much  after  reflexion,  pro- 
ceeding in  the  lines  AD,  BC,  which  will  appear  to  come  from  F,  a 
point  just  as  far  behind  the  mirror  as  R  is  before  it ;  or  if  DA  and 
BC  be  considered  as  two  converging  rays,  they  will  converge  in  the 
same  degree  after  reflexion  in  the  lines  AR,  BR,  and  will  meet  in  R, 
a  point  just  as  far  before  the  mirror,  as  the  point  P,  towards  which 
they  tended,  is  behind  it. 

484.  When  an  object  is  placed  before  a  plane  mirror,  the  image 
of  it  appears  at  the  same  distance  behind  it,  of  the  same  magnitude, 
and  equally  inclined  to  it. 


REFLEXION    OF    LIGHT. 


267 


A 


Let  MN,  (Fig.  99.)  be  a  plane  mir- 
ror, and  AB  an  object  before  it,  the  eye 
being  situated  at  /H.  Now  from  every 
point  in  the  object  innumerable  rays  of 
light  are  constantly  emanating  which  stri- 
king on  all  parts  of  the  mirror,  are  re- 
flected off  again  in  various  directions. 
All  that  is  essential  to  vision  is  that  a 
sufficient  number  of  these  should  be  con- 
veyed to  the  eye.  To  avoid  the  confu- 
sion that  arises  from  the  representation 

of  a  great  number  of  lines,  we  will  consider  those  rays  only  which 
flow  from  the  extreme  parts  of  the  object;  the  rays  proceeding 
from  the  intermediate  points  will  of  course  lie  between  these.  From 
the  point  A,  then,  we  may  conceive  of  a  vast  number  of  rays  of  light 
as  proceeding  to  all  parts  of  the  mirror,  from  which  they  are  reflec- 
ted again  in  various  directions ;  but  those  only  which  fall  upon  the 
small  part  of  the  mirror  FG,  namely  AF,  AG,  are  conveyed  to  the 
eye.  These  therefore  are  the  rays  which  serve  to  make  the  point  A 
visible ;  and  since  they  come  to  the  eye  as  though  they  diverged  from 
a  point  a  as  far  behind  the  mirror  as  A  is  before  it,  the  point  A  will 
appear  as  though  it  were  at  a.  For  the  same  reason  the  point  B  will 
be  rendered  visible  by  the  rays/H,  gH9  which  appear  to  diverge 
from  b  a  point  as  far  behind  the  mirror  as  B  is  before  it.  All  the 
other  points  in  the  line  AB  will  take  their  respective  places  in  the 
line  ah,  which  will  therefore  form  an  exact  image  or  picture  of  the 
object,  affecting  the  eye  in  the  same  manner  as  the  object  would  do 
in  its  place.  It  i§  important  to  remember,  that  how  many  reflexions 
soever  light  may  undergo  in  passing  from  the  object  to  the  eye,  the 
image  will  be  determined  as  to  position,  magnitude,  fyc.  by  the  man- 
ner in  which  the  rays  finally  reach  the  eye  after  the  last  reflexion. 

485.  When  a  plane  mirror  (as  a  common  dressing  glass)  is  turned 
on  an  axis,  the  image  revolves  twice  as  fast  as  the  mirror.  By  turn- 
ing a  mirror  through  45°,  the  image  is  carried  through  90°,  so  that 
a  mirror  set  at  an  angle  of  45°  with  the  horizon  represents  horizon- 
tal objects  in  a  perpendicular  position,  and  perpendicular  objects  on 
a  horizontal  level. 


268 


OPTICS. 


486.  When  an  object  is  placed  between  two  PARALLEL  plane  reflect- 
ors, a  row  of  images  is  formed  in  each  mirror,  appearing  in  a  straight 
line  behind  each  other  to  an  indejinite  extent. 

Let  there  be  two  plane  reflectors,  parallel  to  each  other ;  and  let 
an  object,  a  candle  for  example,  be  placed  between  them.  An  im- 
age of  the  candle  will  be  formed  in  each  mirror,  as  far  behind  it  as  the 
object  is  before  it.  Again  each  of  these  images  becomes  in  its  turn 
a  new  object  to  the  opposite  mirror,  and  forms  a  corresponding  im- 
age as  far  behind  that  mirror  as  it  is  itself  before  it,  and  thus  the  im- 
ages are  repeated  in  a  right  line  until  the  light  becomes  too  feeble  to 
be  visible.  Thus  let  AB,  CD,  (Fig.  100.)  be  two  plane  mirrors, 
and  E  an  object  between  them  :  two  images  will  be  formed  of  E  at 
E'  and  E' ;  two  more  of  E'  and  E7  at  E"  E" ;  and  thus  a  succes- 

Fig.  100. 
A  C 


B 


D 


sion  of  images  will  arise  to  an  indefinite  extent ;  but  since  a  certain 
part  of  the  light  is  lost  at  every  reflexion,  each  succeeding  image  is 
fainter  than  the  preceding.  The  Endless  Gallery  is  formed  on 
this  principle.  It  consists  of  a  box  in  the  opposite  sides  of  which 
are  placed  two  parallel  reflectors,  and  between  them  a  number  of  im- 
ages are  placed,  which  are  repeated  in  an  endless  succession. 

487.  If  an  object  be  placed  between  two  plane  reflectors  INCLINED  to 
each  other,  the  images  formed  will  lie  in  the  circumference  of  a  circle, 

The  common  dressing  glasses  which  are  mounted  on  mahogany 
frames,  and  turn  on  pivots  fixed  in  the  two  ends,  are  convenient  for 
performing  this  experiment.  Two  such  mirrors  may  be  placed  side 
by  side  and  a  candle  set  between  them.  When  the  mirrors  face 
each  other,  that  is,  are  parallel,  an  indefinite  number  of  images  of 


REFLEXION    OF    LIGHT.  269 

the  candle  may  be  seen  in  each  mirror ;  but  on  turning  the  mir- 
rors so  as  to  bring  their  parallel  edges  at  the  bottom  near  each  other 
while  the  upper  edges  are  turned  outwards,  a  circular  row  of  images 
will  be  observed,  the  circle  continually  enlarging  as  the  mirrors  are 
brought  nearer  to  parallelism,  and  contracting  more  and  more  as  the 
inclination  of  the  mirrors  is  increased. 

488.  The  degree  of  perfection  in  the  polish  and  figure  of  a  plane 
speculum,  may  easily  be  known  by  observing  whether  the  images 
seen  in  all  positions,  especially  in  very  oblique  ones,   and  from  all 
parts  of  the  speculum,  appear  exactly  equal  and  similar  to  the  ob- 
jects ;  that  is,  whether  the  images  (more  particularly  of  the  most  dis- 
tant objects)  in  the  room,  appear  naturally,  without  having  any  part 
of  them  distorted ;  when  this  is  the  case,  the  speculum  may  be  pro- 
nounced to  be  a  perfect  one.     The  straight  edges  of  the  rails  of 
wainscot  are  the  best  objects  for  this  experiment.     A  mirror  must 
be  exceedingly  bad  that  will  distort  the  face  of  a  person  looking  into 
it,  because  the  rays  being  returned  almost  directly  back  to  the  eye, 
small  aberrations  will  not  be  rendered  sensible ;  but  let  two  persons 
look  at  each  other's  image  as  obliquely  as  they  can,  and  they  will 
soon  perceive  whether  or  not  the  figure  of  the  speculum  is  defective. 

-In  all  speculums,  the  better  they  are  polished,  other  circumstances 
being  the  same,  the  brighter  will  be  the  images;  that  is  the  more  light 
an  eye  will  receive  from  a  given  object,  which  will  enable  us  to  ex- 
amine the  goodness  of  speculums,  as  to  their  polish,  whenever  we 
have  an  opportunity  of  comparing  several  of  the  same  sort,  and  in  the 
same  light  together.  We  may  also  observe  that  cateris  paribus, 
the  darker  the  color  of  the  speculum  is,  the  better  is  the  polish ;  for 
the  glass  itself  can  be  no  otherwise  seen  than  by  the  reflexions  of 
those  particles  which  have  irregular  positions  with  respect  to  the  rest 
of  the  surface.  But  different  glasses  though  equally  well  polished, 
will  not  always  appear  equally  dark ;  generally,  however,  the  above 
rule  may  be  observed. 

489.  It  is  found  by  experiment,  that  when  a  pencil  of  light  is  in- 
cident perpendicularly  upon  water,  only  18  rays  out  of  1000  are  re- 
flected while  the  greater  part  of  the  remaining  rays  are  transmitted. 
As  the  angle  of  inclination  is  increased,  the  proportion  of  rays  re- 


270 


OPTICS. 


fleeted  is  also  rapidly  increased,  till  at  an  angle  of  75°  the  reflexion  is 
211  rays;  at  85°,  501 ;  and  at  89°,  692.  In  glass  25  out  of  1000 
are  reflected  at  a  perpendicular  incidence ;  and  the  glass  always  re- 
flects more  light  than  water,  till  we  reach  very  great  angles  of  inci- 
dence such  as  S7J°,  when  it  reflects  only  584  rays,  while  water  re- 
flects 614. 

Reflexion  of  Light  from  Concave  Mirrors. 

490.  The  office  of  concave  reflectors,  in  general,  is  to  collect  rays 
of  light.  Hence,  when  applied  to  parallel  rays,  it  makes  them  con- 
verge to  a  focus ;  when  applied  to  rays  already  converging,  it  makes 
them  converge  more ;  to  diverging  rays,  it  makes  them  diverge  less, 
or  overcomes  their  divergency  so  completely  as  to  make  them  par- 
allel, or  eveji  converging. 

By  keeping  steadily  in 
mind  the  proposition,  that  the 
angle  which  the  incident  ray 
makes  with  a  perpendicular 
to  the  reflecting  surface  is 
equal  to  that  which  the  re- 
flected ray  makes  with  the 
same  perpendicular  on  the 
other  side,  the  various  modes 
in  which  light  is  reflected 
from  a  concave  surface  will 
be  readily  understood  from 
the  annexed  figure. 

Let  c  c  c  represent  a  con- 
cave mirror,  whose  center  is 
C,  and  radius  of  curvature 
Cc;  (which  radius  it  must 
be  remembered  is  always 
perpendicular  to  the  curve ;) 
then  the  various  cases  will  be 
as  follqws : 

Parallel  rays,  /c,/c,  will 
pass  to  the  other  side  of  the 


REFLEXION    OF    LIGHT.  271 

/ 

perpendicular  and  meet  in  F,*  which  is  half  way  from  the  mirror 
to  its  center  C. 

Rays  diverging  from  a  point  more  remote  than  the  center -,  Ac,  Ac, 
making  a  less  angle  with  the  perpendiculars  than  the  parallel  rays 
make,  will  also  make  a  less  angle  on  the  other  side  of  the  perpen- 
diculars, meeting  in  a,  between  the  focus  and  the  center. 

Rays  diverging  from  the  center,  Cc,  Cc,  will  be  reflected  back  to 
the  center  again. 

If  we  now  pass  to  the  other  side  of  the  center,  we  see  that  rays 
which  diverge  from  a  point  between  the  center  and  the  focus,  as 
from  0,  converge  to  a  point  on  the  other  side  of  the  center,  as  A. 
Rays  diverging  from  the  focus,  go  out  parallel,  as  c/,  cf. 

Rays  that  come  to  the  mirror  converging,  as  dc,  dc,  meet  in  a 
point  between  the  focus  and  the  mirror,  as  at  D,  and  when  diverging 
from  this  point  they  return  in  the  lines  cd,  cd,  appearing  to  proceed 
from  a  point  behind  the  mirror,  as  Ax,  which  is  called  the  virtual 
focus. 

491.  The  following  experiments,  which  may  be  easily  repeated, 
will  serve  to  render  familiar  the  different  modes  in  which  images  are 
formed  by  concave  mirrors.  See  Fig.  101. 

We  will  suppose  a  lighted  candle  to  be  placed  very  near  to  a  con- 
cave mirror : — it  will  form  no  image  before  it  because  the  rays  go  out 
still  diverging,  but  we  see  an  enlarged  image  of  the  candle  behind  the 
mirror.  As  the  radiant  is  withdrawn  from  the  mirror  towards  the 
principal  focus,  the  image  will  rapidly  recede  on  the  other  side,  and 
grow  larger  and  larger  until  the  radiant  reaches  the  focus,  when  the 
image  will  suddenly  disappear.  On  removing  the  radiant  a  little  far- 
ther, the  image  will  be  found  at  a  great  distance  before  the  mirror  and 
very  much  enlarged.  As  the  radiant  approaches  the  center,  the  im- 
age approaches  it  rapidly  on  the  other  side  of  it,  constantly  diminish- 
es in  size  until  they  both  meet  and  coincide  in  the  center.  Removing 
the  radiant  still  farther,  the  image  appears  again  between  the  center 
and  the  focus,  diminished  in  size,  and  slowly  approaching  the  focus 
as  the  radiant  recedes  but  never  reaches  it,  unless  when  the  radiant 
may  be  considered  as  at  an  infinite  distance,  as  in  the  case  of  the 
heavenly  bodies. 


*  F  is  called  the  focus  of  parallel  rays. 


272  OPTICS* 

i 

One  who  looks  into  a  concave  mirror  sees  his  own  face  varied  in  the 
following  manner.  When  he  holds  the  reflector  near  to  his  face,  he 
sees  his  image  distinct,  because  the  rays  come  to  the  eye  diverging 
(which  is  their  natural  state  with  respect  to  near  objects,)  and  enlarged, 
because,  as  the  rays  diverge  less  than  before,  the  image  is  thrown  back 
to  a  greater  distance  behind  the  mirror  than  the  object  is  before  it,  and 
the  magnitude  is  proportioned  to  that  distance.  As  he  withdraws  the 
eye,  the  image  grows  larger  and  larger  until  the  eye  reaches  the  fo- 
cus. From  the  focus  to  the  center,  no  distinct  image  is  seen,  be- 
cause the  rays  come  to  the  eye  converging,  a  condition  incompatible 
with  distinct  vision.  At  the  center  the  eye  sees  only  its  own  image, 
since  the  image  is  reflected  back  to  the  object  and  coincides  with  it. 
Beyond  the  center,  his  face  will  be  seen  on  the  other  side  of  the  cen- 
ter before  the  mirror  (though  habit  may  lead  him  to  refer  it  to  a  point 
behind  it ;)  and  it  will  be  diminished,  being  nearer  to  the  mirror  than 
the  object  is,  and  inverted,  because  an  inverted  image  is  formed  when 
the  rays  are  brought  to  a  focus,  and  this  becomes  the  object  which  is 
seen  by  the  eye.* 

492.  Concave  mirrors,  in  consequence  of  the  property  they  have 
of  forming  images  in  the  air,  were  in  a  less  enlightened  age  than  the 
present,  frequently  employed  by  showmen  for  exhibiting  surprising 
appearances.  The  mirror  was  usually  concealed  behind  a  wall,  and 
the  object,  which  might  be  a  skull,  a  dagger,  Sic.  was  placed  between 
it  and  the  wall  and  strongly  illuminated.  The  rays  proceeding  from 
the  object  fell  upon  the  mirror  and  were  reflected  by  it  through  an 
opening  through  the  wall,  and  brought  to  a  focus  so  as  to  form  an  im- 
age in  the  same  room  with  the  spectator.  If  a  fine  transparent  cloud 
of  blue  smoke  is  raised,  by  means  of  a  chafing  dish,  around  the  fo- 
cus of  a  large  concave  mirror,  the  image  of  any  highly  illuminated 
object  will  be  depicted  in  the  middle  of  it  with  great  beauty.  A  dish 
of  fruit  thus  represented  invites  the  spectator  to  taste,  but  the  instant 
he  reaches  out  his  hand  a  drawn  dagger  presents  itself. 


*  These  phenomena  may  be  all  observed  with  an  ordinary  concave 
shaving  glass. 


REFLEXION  OF  LIGHT  FROM  CONVEX  SURFACES.      273 

493.  Concave  mirrors  have  been  used  as  light  house  reflectors,  and 
as  burning  instruments.     When  used  in  light  houses,  they  are  form- 
ed of  copper  plated  with  silver,  and  they  are  hammered  into  a  par- 
abolic form,  and  then  polished  with  (he  hand.     A  lamp  placed  in  the 
focus  of  the  parabola,  will  have  its  divergent  light  thrown,  after  re- 
flexion, into  something  like  a  parallel  beam,  which  will  retain  its  in- 
tensity to  a  great  distance. 

When  concave  mirrors  are  used  for  burning,  they  are  generally- 
made  spherical,  and  regularly  ground  and  polished  upon  a  tool,  like 
the  specula  used  in  telescopes.  The  most  celebrated  of  these  were 
made  by  M.  Villele,  of  Lyons,  who,  executed  five  large  ones.  One 
of  the  best  of  them,  which  consisted  of  copper  and  tin,  was  very 
nearly  four  feet  in  diameter,  and  its  focal  length  thirty  ei^ht  inches. 
It  melted  the  metals,  as  silver  and  copper,  and  even  some  of  the  more 
infusible  earths. 

Burning  mirrors,  however,  have  sometimes  been  constructed  on  a 
much  larger  scale  by  combining  a  great  number  of  plane  mirrors. 
It  is  supposed  that  it  was  a  mirror  of  this  kind  which  Archimedes  em- 
ployed in  setting  fire  to  the  Roman  fleet  under  Marcellus.  Athana- 
sius  Kircher,  who  first  proved  the  efficacy  of  a  union  of  plane  mir- 
rors, went  with  his  pupil  Scheiner  to  Syracuse,  to  examine  the  posi- 
tion of  the  hostile  fleet ;  and  they  were  both  satisfied  that  the  ships 
of  Marcellus  could  not  have  been  more  than  thirty  paces  distant  from 
Archimedes. 

Buffon,  the  celebrated  naturalist,  constructed  a  burning  apparatus 
upon  this  principle,  which  may  be  easily  explained.  He  combined 
one  hundred  and  sixty  eight  pieces  of  mirror  six  inches  by  eight,  so 
that  he  could,  by  a  little  mechanism  connected  with  each,  cause 
them  to  reflect  the  light  of  the  sun  upon  one  spot.  Those  pieces  of 
glass  were  selected  which  gave  the  smallest  image  of  the  sun  at  two 
hundred  and  fifty  feet.  With  one  hundred  and  fifty  four  mirrors, 
he  was  able  to  fire  combustibles  at  the  distance  of  two  hundred  and 
fifty  feet. 

Reflexion  of  Light  from  Convex  Surfaces. 

494.  The  office  of  a  convex  reflector  is,  in  general,  to  separate 
rays  of  light.     Hence,  when  applied  to  parallel  rays,  it  makes  them 
diverge^  to  diverging  rays  it  makes  them  diverge  more,  and  to  con- 

35 


274 


OPTICS. 


Fig.  102. 


verging  rays,  it  makes  them  converge 
less,  even  so  much  less,  sometimes, 
as  to  become  parallel  or  diverging. 

Thus  (Fig.  102.)  the  parallel  rays 
AM,  AN,  falling  upon  the  convex  mir- 
ror  MN  are  reflected  to  the  other  side 
of  the  perpendiculars,  CE,  CE,  into 
the  diverging  lines  MB,  NB,  which 
appear  to  come  from  F  behind  the 
mirror,  which  point  is  called  the  vir- 
tual focus. 

In  like  manner  the  di- 
verging rays  AM,  AN, 
(Fig.  103.)  are  rendered 
more  diverging  than  before, 
,and  appear  to  come  from  a 
point  F  nearer  the  mirror 
than  the  focus  of  parallel 
rays. 


495.  When  an  object  is  placed  before  a  convex  mirror,  the  image 
of  it  appears  nearer  to  the  surface  of  the  mirror  than  the  object,  and 
of  a  less  size. 

Thus  (Fig.  104.)  AB  is  seen  by  the  F]g-  104- 

eye  at  ab,  and  the  rays  from  every  point 
in  AB  being  rendered  more  divergent  by 
reflexion  they  will  appear  to  come  from 
a  nearer  object ;  and  since  the  extreme 
points  a  and  b,  are  nearer  to  each  other 
than  AB,  the  image  will  be  smaller  than 
the  object. 

Convex  mirrors  exhibit  their  peculiar 
properties  in  the  diminished  representa- 
tion which  they  give  of  the  furniture  of 
a  room ;  and  as  objects  sometimes  appear  more  interesting  and  beau- 
tiful in  miniature,  hence  the  application  of  such  mirrors  for  parlor 
glasses. 


REFRACTION    OF    LIGHT. 


275 


CHAPTER  II. 

OF  THE  REFRACTION  OF  LIGHT,  AND  OF  LENSES  AND  PRISMS. 

496.  When  light  passes  out  of  one  medium  into  another  it  is  turn- 
ed out  of  its  course,  or  refracted,  according  to  the  following  law  : 

Light,  in  passing  out  of  a  rarer,  into  a  denser  medium,  is  refrac- 
ted towards  a  perpendicular  to  that  medium  ;  and  in  passing  out  of 
a  denser  into  a  rarer  medium,  it  is  refracted  from  the  perpendiculaf. 


Thus  if  ab  (Fig.  105.)  be  the  surface 
of  a  vessel  of  water,  a  ray  of  light  AB, 
passing  out  of  air  (a  rarer)  into  water  (a 
denser  medium)  will  not  pass  in  the  di- 
rection of  BC,  but  will  be  turned  towards 
the  perpendicular  EB,  and  pass  through 
the  water  in  the  line  BD ;  passing  out  of 
water  into  air,  it  will  be  turned  away  from 
the  perpendicular  BF,  and  pass  through 
the  air  in  the  direction  of  BA. 


D   E 


497.  We  see  an  example  of  the  foregoing  principle  in  the  bent 
appearance  of  an  oar  in  the  water,  the  light  of  the  part  immersed  (by 
which  it  is  visible)  being  turned  from  the  perpendicular,  and  causing 
it  to  appear  higher  than  its  true  place ;  for  objects  appear  in  the  di- 
rection in  which  the  rays  of  light  emanating  from  them  finally  come 
to  the  eye.  In  the  same  manner,  the  bottom  of  a  river  appears 
elevated,  and  diminishes  the  apparent  depth  of  the  stream.  Per- 
sons have  sometimes  been  drowned  in  consequence  of  venturing  into 
water,  that  appeared,  from  the  apparent  elevation  of  the  bottom, 
much  shallower  than  it  was.  The  following  ancient  experiment  illus- 
trates the  same  principle.  If  a  small  piece  of  silver  be  placed  in 
the  bottom  of  a  bowl,  and  the  eye  be  withdrawn  until  the  piece  of 
silver  disappears,  on  filling  up  the  bowl  with  water,  the  silver  comes  ' 
into  view. 


498.  Transparent  bodies  differ  much  among  themselves  in  refract- 
ing  potver.     That  is,  some  bodies  have  the  power  of  changing  the 


276 


OPTICS. 


Fig.  106. 


direction  of  light  much  more  than 
others.  Thus  when  a  ray  of  light 
AN,  (Fig.  106.)  passes  into  water 
it  will  be  turned  into  the  line  ND  ; 
if  the  medium  he  sulphur,  which 
is  denser  than  water,  the  direction 
of  the  light  will  be  changed  more, 
being  refracted  farther  towards 
the  perpendicular  into  the  line 
NF  ;  and  if  the  medium  be  dia- 
mond the  change  will  be  greater 
still,  the  refraction  being  in  the 
line  NH. 

Among  different  bodies,  certain  salts  of  silver  and  lead,  the  dia- 
mond, phosphorus,  and  sulphur,  rank  highest  in  refracting  power  ; 
next  come  the  precious  gems,  and  flint  glass,  containing  a  large  pro- 
portion of  the  oxide  of  lead,  which  has  a  refracting  power  conside- 
rably higher  than  crown  glass,  containing  less  metallic  oxide  ;  to 
which  succeed  the  aromatic  oils.  Among  transparent  solids,  fluor 
spar  is  distinguished  for  its  low  refracting  powers;  but  tabasheer,  a 
substance  formed  from  the  concreted  juice  of  the  Indian  bamboo,  is 
more  particularly  remarkable  for  this  property. 

499.  LENSES,  on  account  of  their  extensive  use  in  the  construction 
of  optical  instruments,  require  very  particular  attention  in  the  study 
of  Optics.  They  are  of  several  varieties,  as  is  shown  in  the  follow- 
ing figure. 

A  double  convex  lens  (A)  is  a  solid 
formed  by  two  segments  of  a  sphere  ap- 
plied base  to  base.* 

A  plano-convex  lens  (B)  is  a  lens 
having  one  of  its  sides  convex  and  the 
other  plane,  being  simply  a  segment  of  a  sphere. 


Fig.  107. 


F  E 


B    A 


*  Though  this  is  the  most  common  form  of  the  double  convex  lens, 
yet  it  is  not  essential  that  the  two  segments  should  be  portions  of  the 
same  spheres  they  may  be  segments  of  different  spheres  in  which 
ea*e  the  curvatures  will  be  unequal  on  the  two  sides  ef  the  lens. 


REFRACTION    OF    LIGHT.  277 

A  double  concave  lens  (C)  is  a  solid  bounded  by  two  concave 
spherical  surfaces,  which  may  be  either  equally  or  unequally  concave. 

A  plano-concave  lens  (D)  is  a  lens  one  of  whose  surfaces  is  plane 
and  the  other  concave. 

A  meniscus  (E)  is  a  lens,  one  of  whose  surfaces  is  convex  and 
the  other  concave,  but  the  concavity  being  less  than  the  convexity, 
it  takes  the  form  of  a  crescent,  and  has  the  effect  of  a  convex  lens 
whose  convexity  is  equal  to  the  difference  between  the  sphericities 
of  the  two  sides. 

A  concavo-convex  lens  (F)  is  a  lens  one  of  whose  surfaces  is  con- 
vex and  the  other  concave,  the  concavity  exceeding  the  convexity, 
and  the  lens  being  therefore  equivalent  to  a  concave  lens  whose 
sphericity  is  equal  to  the  difference  between  the  sphericities  of  the 
two  sides. 

A  line  (MN)  passing  through  the  center  of  a  lens  perpendicular 
to  its  opposite  surfaces,  is  called  the  axis. 

500.  The  office  of  a  convex  lens  is  to  COLLECT  rays  of  light. 
Hence,  when  applied  to  parallel  rays,  it  makes  them  converge ;  to 
diverging  rays,  it  makes  them  diverge  less ;  and  to  converging  rays, 
it  makes  them  converge  more.     Moreover,  with  regard  to  diverging 
rays,  the  degree  of  divergence  may  be  reduced  so  much  as  to  ren- 
der the  rays  parallel,  or  even  to  make  them  converge,  which  will 
depend  both  on  the  position  of  the  radiant  and  on  the  power  of  the 
lens. 

On  the  contrary,  the  office  of  a  concave  lens  is  to  SEPARATE  rays 
of  light.  Hence,  when  it  is  applied  to  parallel  rays,  it  makes  them 
diverge;  to  rays  already  diverging,  it  makes  them  diverge  more; 
and  to  converging  rays,  it  makes  them  converge  less,  become  par- 
allel, or  even  diverging^ 

501.  With  these  general  priciples  in  view,  we  may  now  advanta- 
geously investigate  the  manner  in  which  IMAGES  are  formed  by  means 
of  lenses. 

1.  If  we  place  a  radiant,  as  a  candle,  nearer  to  a  lens  than  its 
principal  focus,  then,  since  the  rays  go  out  diverging,  no  image  will 
be  formed  on  the  other  side  of  the  lens. 

2.  If  we  place  the  radiant  in  the  focus,  the  rays  will  go  out  par- 
allel, but  will  still  not  be  collected  into  a  distinct  image. 


278  .  OPTICS. 

3.  If  the  radiant  is  removed  farther  from  the  lens  than  its  princi- 
pal focus,  then  the  rays  will  be  collected  on  the  other  side  of  the  lens 
so  as  to  form  a  distinct  representation  of  the  object. 

As  this  last  case  is  particularly  important,  since  it  exhibits  the  man- 
ner in  which  images  are  formed  by  means  of  convex  lenses,  let  us 
examine  it  with  more  attention. 

502.  Rays  of  light  diverging  from  the  several  points  of  any  ob- 
ject, which  is  farther  from  a  convex  lens  than  its  principal  focus,  will 
be  made  to  converge  on  the  other  side  of  the  lens,  to  points  corres- 
ponding to  those  from  which  they  diverged,  and  will  form  an  image. 

Let  MN  (Fig.  108.)  be  a  Fig>  108. 

luminous  object  placed  before 
a  double  convex  lens  L  L. 
Now  every  point  in  the  radi- 
ant sends  forth  innumerable  . 
rays  in  every  direction,  part 
of  which  fall  upon  the  lens 
LL.  Each  pencil  may  be 
considered  as  a  cone  of  rays, 
having  for  its  axis  the  straight  line  which  passes  through  the  center  of 
the  lens,  which  line  suffers  no  change  of  direction,  while  those  rays  of 
the  pencil  which  strike  upon  the  extreme  parts  of  the  lens;  form  the 
exterior  rays  of  the  cone :  all  the  others  are  of  course  included  be- 
tween these.  It  will  be  sufficient  to  follow  the  course  of  the  central 
and  the  two  extreme  rays.  Let  ML,  MC,  ML  represent  such  a 
pencil.  The  two  extreme  rays  will  be  collected  by  the  lens  and 
made  to  meet  in  the  axis  or  central  ray  in  some  point  on  the  other 
side,  as  at  m.  For  the  same  reason,  every  other  point  in  the  object 
will  have  its  corresponding  point  in  the  image,  and  all  these  points  of 
the  image  taken  together,  form  a  true  representation  of  the  object.  By 
inspecting  the  figure,  it  will  be  seen  that  the  axes  of  all  the  pencils 
cross  each  other  in  the  center  of  the  lens ;  that  the  image  corres- 
ponding to  the  top  of  the  object  is  carried  to  the  bottom  of  the  image, 
while  tfcat  corresponding  to  the  bottom  of  the  object  is  at  the  top  of 
the  image,  and,  consequently,  that  th£  image  is  inverted  with  respect 
to  the  object.  It  will  be  farther  seen,  that  although  the  individual 
rays  which  make  up  a  single  pencil  are  made,  on  passing  through 


REFRACTION    OF    LIGHT.  279 

the  lens,  to  converge,  yet  the  axes  of  all  the  pencils  go  out  diverg- 
ing from  each  other,  which  carries  them  farther  and  farther  asunder, 
the  farther  they  proceed  before  they  come  to  a  focus.  Hence,  the 
farther  the  image  is  formed  behind  the  lens,  the  greater  will  be  its 
diameter. 

The  diameter  of  the  image  will  not  be  altered  by  changing  the 
area  of  the  lens :  for  that  diameter  will  be  determined  in  all  cases 
by  the  distance  between  the  axes  of  the  two  pencils  which  come 
from  the  extremities  of  the  object  and  cross  each  other  in  the  center 
of  the  lens.  The  size  of  the  image,  however,  will  be  affected  by 
changing  the  convexity  of  the  lens,  while  the  object  remains  the  same 
and  at  the  same  place. 

503.  Rays  proceeding  from  any  radiant  point  which  are  refracted 
by  the  different  parts  of  the  same  lens,  do  not  meet  accurately  in  one 
focus,  but  their  points  of  meeting  are  spread  over  a  certain  space, 
whose  diameter  is  called  the  SPHERICAL  ABERRATION  of  the  lens. 

Let  LL  be  a  piano-con-    * ^  Fig>  109' 

vex  lens,  on  which  are  in- 
cident the  parallel  rays  RL,  ^ 
RL  at  the  extremities,  and 

R'L7,  R'L'  near  the  axis;  

the   axis   will    proceed   on  "R  L 

without  any  change  of  direction,  and  the  rays  which  are  very  near 
to  the  axis,  being  also  nearly  perpendicular  to  the  refracting  surface, 
sustain  only  a  slight  change  of  direction,  sufficient,  however,  to  col- 
lect them  into  a  focus  at  some  distance  from  the  lens  in  the  point  F. 
But  the  rays  RL,  RL,  meeting  the  refracting  surface  more  oblique- 
ly, are  more  turned  out  of  their  course,  and  are  therefore  collected 
into  a  focus  in  some  point  nearer  to  the  lens  than  F,  as  at  /.  The 
intermediate  rays  refracted  by  the  lens  will  have  their  foci  between 
F  and  /.  Continue  the  lines  L/*and  L/,  till  they  meet  at  G  and  H, 
a  plane  passing  through  F.  The  distance  /F  is  called  the  longitu- 
dinal spherical  aberration,  and  GH  the  lateral  spherical  aberration. 

It  is  obvious  that  such  a  lens  oannot  form  a  distinct  picture  of  any 
object  in  its  focus  F.  If  it  is  exposed  to  the  sun,  the  central  parts 
of  the  lens  L'wzL',  whose  focus  is  at  F,  will  form  a  pretty  bright  im- 
age of  the  sun  at  F;  but  as  the  rays  of  the  sun  which  pass  through 


280  OPTICS. 

the  outer  part  LL  of  the  lens  have  their  foci  at  points  between /and 
F,  the  rays  will,  after  arriving  at  these  points,  pass  on  to  the  plane 
GH,  and  occupy  a  circle  whose  diameter  is  GH ;  hence  the  image  of 
the  sun  in  the  focus  F  will  be  a  bright  disk,  surrounded  and  rendered 
indistinct  by  a  broad  halo  of  light  growing  fainter  and  fainter  from  F 
to  G  and  H.  In  like  manner,  every  object  seen  through  such  a  lens, 
and  every  image  formed  by  it,  will  be  rendered  confused  and  indis- 
tinct by  spherical  aberration. 

If  we  cover  up  all  the  exterior  portions  of  the  lens,  so  as  to  per- 
mit only  those  portions  of  the  rays  which  lie  near  the  axis  to  pass 
through  the  lens,  then  the  rays  all  meet  at  or  very  near  to  the  point 
F,  and  a  much  more  distinct  image  is  formed ;  but  so  much  of  the 
light  is  excluded  by  this  process,  that  the  brightness  of  the  image  is 
considerably  diminished.  The  dimensions  of  the  image  are  the  same 
in  both  cases. 

504.  The  Prism  is  an  important  instrument  in  Optics,  especially 
as  it  affords  the  means  of  decomposing  light,  and  enters  into  the  con- 
struction of  several  optical  instruments.  The  triangular  prism  is 
the  only  one  employed  in  experiments,  and  of  this  nothing  more  is 
essential  than  barely  the  inclination  of  two  plane  transparent  surfaces 
to  one  another.  The  optical  prism,  however,  is  usually  understood 
to  be  a  piece  of  solid  glass,  having  two  sides  constituted  of  equal 
parallelograms,  and  a  third  side  called  the  base.  The  line  of  inter- 
section of  the  two  sides  is  called  the  edge,  and  the  angle  contained 
by  the  sides,  the  refracting  angle  of  the  prism.  A  straight  line 
passing  lengthwise  of  the  prism,  through  its  center  of  gravity  and 
parallel  to  the  edge,  is  called  the  axis.  A  section  made  by  a  plane 
perpendicular  to  the  axis,  is  an  isosceles  triangle.  Frequently,  the 
three  angles  of  the  prism  are  made  equal  to  one  another,  each  be- 
ing 60°.* 

*  A  very  convenient  prism  for  common  experiments  may  be  con- 
structed as  follows.  Select  two  plates  of  window  glass  of  the  best 
quality,  or  better,  two  pieces  of  looking  glass,  from  which  the  silver- 
ing has  been  removed.  The  plates  may  be  five  or  six  inches  long, 
and  one  and  a  half  or  two  inches  broad.  They  are  to  be  united  at 
their  edges  at  an  angle  of  about  60°,  and  furnished  with  a  tin  case, 


THE    SOLAR    SPECTRUM.  281 

Figure  110  represents  a  sec-  Fig.  no. 

lion  of  a  prism  ABC,  of  which 
AB  is  the  base,  and  ACB  the 
refracting  angle.  DE  is  a  beam 
of  the  sun's  light  falling  obliquely 
on  the  first  surface  AC,  where 
one  portion  is  reflected  but  an- 
other portion  transmitted.  The 

latter  portion,  instead  of  passing  directly  forward  and  forming  an 
image  of  the  sun  at  H,  is  turned  upward  towards  the  perpendicular 
pp',  meeting  the  opposite  surface  CB  in  F,  where  it  is  again  turned 
upward  from  the  perpendicular  p'p  in  the  direction  FG,  carrying  the 
image  of  the  sun  from  H  to  G. 


CHAPTER  III. 

OF  THE  SOLAR  SPECTRUM,  OF  THE  RAINBOW,  AND  OF  COLORS  IN 
NATURAL  OBJECTS. 

505.  In  tracing  the  course  of  rays  of  light  through  a  refracting 
medium,  we  have  thus  far  supposed  them  to  be  homogeneous,  and 
to  be  all  affected  in  the  same  manner.  But  in  nature  the  fact  is  oth- 
erwise ;  that  is, 

The  sun's  light  consists  of  rays  which  differ  in  refrangibilily  and 
in  color. 

The  glass  prism,  in  consequence  of  the  strong  refraction  of  light 
which  it  produces,  (see  Art.  504.)  is  well  fitted  for  experiments  of 


which  shall  afford  the  base  and  the  two  ends,  and  a  covering  for  the 
edge.  One  of  the  ends  has  an  orifice  with  a  stopper,  for  the  conven- 
ience of  filling  with  a  fluid,  which  may  be  pure  water,  or  better,  a 
saturated  solution  of  the  sugar  of  lead  filtered  perfectly  clear.  Pro- 
jections may  be  attached  to  the  two  ends  to  serve  as  handles  or  as  an 
axis  on  which  the  prism  may  rest  on  supports.  Instead  of  the  tin 
case,  we  may  employ  a  block  of  hard  wood,  first  formed  into  a  tri- 
angular prism,  and  then  dug  out  so  as  to  admit  the  plates. 

36 


282 


OPTICS. 


this  kind.  We  procure,  therefore,  a  triangular  prism  of  good  flint 
glass,  and  having  darkened  a  room,  admit  a  sun  beam  obliquely 
through  a  small  round  hole  in  the  window  shutter.  Across  this 
beam,  near  the  shutter,  we  place  the  prism,  with  its  edge  parallel  to 
the  horizon,  so  as  to  receive  the  beam  upon  one  of  its  sides.  The 
rays,  on  passing  through  the  prism,  will  be  refracted  and  thrown  up- 
wards, as  will  be  rendered  evident  by  conceiving  perpendiculars 
drawn  to  the  surface  of  the  prism  at  the  points  of  incidence  and 
emergence.  If  now  we  receive  the  refracted  rays  upon  a  screen, 
at  some  distance,  they  will  form  an  elongated  image,  exhibiting  the 
colors  of  the  rainbow,  namely,  red,  orange,  yellow,  green,  blue,  in- 
digo, violet,  together  composing  the  prismatic  spectrum.  (See  Fig. 

in.) 

Fig.  111. 


'  S,  a  sun-beam. 

F,  a  hole  in  the  window  shutter. 

ABC,  the  prism,  having  its  refracting  angle  ACB  downwards. 
Y,  a  white  spot,  being  an  image  of  the  sun  formed  on  the  floor  be- 
fore the  prism  is  introduced. 

MN,  the  screen  containing  the  spectrum.* 

A  pleasing  way  of  exhibiting  the  separate  colors  of  the  spectrum, 
is  to  throw  the  prismatic  beam  on  a  distant  wall  or  screen,  so  as  to 


*  The  opposite  white  wall  of  plaster  or  stucco,  may  serve  the  pur- 
pose of  a  screen ;  or  the  screen  may  be  made  of  a  large  sheet  of  white 
paper ;  but  a  convenient  screen  for  the  lecture  room  is  made  by  past- 
ing a  large  sheet  of  drawing  paper  to  a  frame  and  attaching  it  to  a 
movable  stand. 


THE    SOLAR    SPECTRUM. 


283 


form  a  long  spectrum,  and  into  this  beam,  at  some  convenient  dis- 
tance from  the  prism,  to  introduce  a  concave  lens  of  a  size  sufficient 
to  cover  each  of  the  different  colored  pencils  successively.  The 
lens  will  cause  the  rays  of  the  same  color  to  diverge,  and  to  form  a 
circular  image  on  the  screen,  which  will  distinguish  them  very  stri- 
kingly from  the  contiguous  portions  of  the  spectrum. 

506.  If  rays  of  the  same  color  in  the  prismatic  beam  be  insulated 
from  the  rest  and  made  to  pass  through  a  second  prism,  they  are  re- 
fracted as  usual,  (the  amount  of  refraction  being  different  for  the 
different  colored  rays,)  but  they  undergo  no  farther  change  of  color. 

To  perform  this  experiment,  we  provide  a  board,  perforated  with 
a  small  round  hole,  and  mounted  on  a  stand.  This  screen  is  placed 
across  the  prismatic  beam,  a  little  way  from  the  prism,  in  such  a 
manner  as  to  permit  rays  of  the  same  color  only  to  pass  through  the 
aperture,  while  the  other  portions  of  the  beam  are  intercepted.  The 
homogeneous  light  thus  insulated  is  made  to  pass  through  a  second 
prism,  and  its  image  is  thrown  on  the  wall.  The  experiment  will  be 
more  perfect,  if  the  homogeneous  pencil  be  made  to  pass  through  a 
second  screen  similar  to  the  first,  so  as  to  let  only  the  central  rays 
fall  upon  the  second  prism.  This  second  refraction  produces  no 
change  of  color.  It  will  be  found,  however,  that,  while  all  other 
things  remain  the  same,  the  several  images  formed  of  homogeneous 
rays,  will  occupy  different  positions  on  the  wall,  the  red  being  lowest 
and  the  violet  highest,  and  the  intermediate  colors  arranged  between 
them  in  the  order  of  their  refrangibilities.  (See  Fig.  112.) 

Fig.  112. 


In  addition  to  the  parts  of  the  figure  enumerated  in  Fig.  Ill,  DE 
represents  the  first  screen,  which  permits  only  one  sort  of  rays  to  pass 
by  a  small  aperture  at  G,  and  de  represents  a  second  screen,  which 
permits  only  the  central  rays  of  this  pencil  to  pass  by  a  small  hole 


284  OPTICS. 

atg;  a  be  is  the  second  prism,  and  M  is  the  image  of  homogeneous 
light  on  the  wall. 

507.  The  light  of  the  sun  reflected  from  the  first  surface  of  bodies, 
and  also  the  white  flames  of  all  combustibles,  whether  direct  or  re- 
flected, differ  in  color  and  refrangibility,  like  the  direct  light  of  the 
sun. 

The  truth  stated  in  this  proposition  was  established  by  Newton,  by 
experiments  with  the  prism,  similar  to  those  detailed  in  connexion 
with  the  preceding  propositions. 

508.  The  sun's  light  is  compounded  of  all  the  prismatic  colors, 
mixed  in  due  proportion. 

If  we  collect,  by  means  of  a  convex  lens,  the  different  colored 
pencils  in  the  prismatic  beam,  just  after  they  have  emerged  from  the 
prism,  (see  Fig.  111.)  the  image  formed  by  the  lens  will  be  perfect- 
ly white.  A  concave  mirror  may  be  used  instead  of  the  lens,  the 
image  being  thrown  on  a  screen.  Or  the  rays  after  they  have  pass- 
ed the  prism  may  be  received  on  a  second  prism  of  the  same  kind, 
placed  near  the  first,  but  with  its  refracting  angle  in  the  opposite  di- 
rection. In  this  case  the  second  prisrn  restores  the  light  to  its  usual 
whiteness. 

That  all  the  different  colors  of  the  spectrum  are  essential  to  the 
composition  of  white  light,  may  be  rendered  evident  by  intercepting 
a  portion  of  any  one  of  the  colors  of  the  spectrum  before  they  have 
been  re-united  as  in  the  foregoing  experiments.  Thus  if  we  intro- 
duce a  thread  or  a  wire  into  any  part  of  the  prismatic  beam  between 
the  prisrn  and  the  lens,  the  image  formed  by  the  lens  will  be  no  long- 
er white  but  discolored.  If,  instead  of  the  wire,  an  instrument  sha- 
ped like  a  comb  with  coarse  broad  teeth,  be  introduced  into  the 
beam,  the  discoloration  of  the  image  is  more  diversified,  the  col- 
ors of  the  image  being  those  compounded  of  the  prismatic  colors, 
which  are  not  intercepted  by  the  comb.  If  the  teeth  of  the  comb 
be  passed  slowly  over  the  beam,  a  succession  of  different  colors  ap- 
pears, such  as  red,  yellow,  green,  blue  and  purple;  but  if  the  motion 
of  the  comb  be  rapid,  all  these  different  hues  become  blended  into 
one  by  the  momentary  continuance  of  each  in  the  eye,  and  the  sen- 
sation is  that  of  white  light. 


THE    RAINBOW.  285 

509.  For  a  similar  reason,  if  the  colors  of  the  spectrum  are  paint- 
ed on  a  top,  in  due  intensity  and  proportion,  and  the  top  be  set  to  spin- 
ning, the  sensation  will  be  that  of  white  light.     Or  the  colors  of  the 
spectrum  may  be  first  laid  on  a  sheet  of  paper,  and  this  may  be 
pasted  on  a  cylinder  of  wood,  which  may  be  made  to  revolve  on  the 
whirling  tables :  the  result  will  be  the  same.     Newton  tried  various 
experiments  with  different  colored  powders,  grinding  together  such  as 
corresponded   as  nearly  as  possible  to  the  colors  of  the    spectrum. 
By  this  means  he  was  able  to  produce,  from  the  mixture  of  seven 
different  colored  powders,  a  greyish  white,  but  could  never  reach  a 
perfectly  clear  white,  owing  to  the  difficulty  of  finding  powders  whose 
colors  corresponded  exactly  to  those  of  the  spectrum. 

510.  Several  of  the  colors  of  the  spectrum  may  be.  produced  by 
the  mixture  of  other  colors ;  as  green  by  the  union  of  yellow  and 
blue,  orange  by  red  and  yellow,  fyc.     Experiments  were  devised  by 
Newton  for  thus  combining  the  colors  of  two  contiguous  spectrurns, 
transferring  for  example,  the  blue  of  one  to  the  yellow  of  the  other, 
and  forming  green  by  their  union.     On  causing  this  compound  green, 
however,  to  pass  through  the  prism  it  is  resolved  into  its  original  col- 
ors, yellow  and  blue,  whereas,  the  green  of  the  spectrum  is  not  thus 
resolved  by  the  prism.     Hence  Newton  infers  that  the  green  of  the 
spectrum  is  not  a  compound  but  a  simple  original  color,  and  so  of  all 
the  rest. 

511.  The  knowledge  of  the  composition  of  light,  and  of  the  prop- 
erties of  the  solar  spectrum,  naturally  lead  to   an   inquiry  into  the 
subject  of  colors,  as  exhibited  in  the  phenomena  of  nature.     The 
bright  tints  of  the  rainbow,  the  splendid  hues  sometimes  exhibited  by 
thin  plates,  as  soap  bubbles,  and  finally  the  diversified  colors  of  ob- 
jects in  all  the  kingdoms  of  nature,  remained  to  be  accounted   for. 
Some  of  these  we  proceed  to  explain,  but  others  are  of  a  nature  too 
intricate  for  the  present  work. 

The  Rainbow* 

512.  The  rainbow,  one  of  the  most  striking  and  magnificent  of  the 

*  The  theory  of  the  Rainbow  is  necessarily  somewhat  intricate,  and 
possibly  may  prove  too  difficult  for  the  young  learner,  though  we 
shall  endeavor  to  make  it  as  plain  as  possible. 


286  OPTICS. 

phenomena  of  nature,  was  long  ago  supposed  to  be  owing  to  some 
modification  which  the  light  of  the  sun  undergoes  in  passing  into 
drops  of  rain,  but  the  complete  developement  of  the  causes  on  which 
it  depends,  was  reserved  for  the  genius  of  Newton,  and  naturally 
followed  in  the  train  of  those  discoveries  which  he  made  upon  the 
prismatic  spectrum. 

The  rainbow,  when  exhibited  in  its  more  perfect  forms,  consists  of 
two  arches,  usually  seen  in  the  east  during  a  shower  of  rain,  while 
the  sun  is  shining  in  the  west.  These  arches  are  denominated  the 
outer  and  the  inner  bow,  of  which  the  inner  bow  is  the  brighter,  but 
the  outer  bow  is  of  larger  dimensions  every  way.  The  succession 
of  colors  in  the  one  is  directly  opposite  to  that  of  the  other. 

513.  Drops  of  rain,  though  small,  are  large  in  comparison  with 
the  minuteness  of  rays  of  light,  and  are  to  be  regarded  as  spheres  of  wa- 
ter, exerting  the  powers  of  refraction  and  reflexion  in  the  same  man- 
ner as  large  globes  of  water  would  do.  It  was,  in  fact,  by  investiga- 
ting the  manner  in  which  globular  glass  vessels  filled  with  water  mod- 
ify the  solar  rays,  that  the  first  hints  were  obtained  respecting  the 
cause  of  the  rainbow.  In  the  year  1611,  Antonio  de  Dominis  made 
a  considerable  advance  towards  the  theory  of  the  rainbow,  by  suspen- 
ding a  glass  globe  in  the  sun's  light,  when  he  found  that  while  he 
stood  with  his  back  to  the  sun,  the  colors  of  the  rainbow  were  reflect- 
ed to  his  eye  in  succession  by  the  globe,  as  it  was  moved  higher  or 
lower. 

Let  us  therefore,  in  the  first  place,  follow  the  course  of  a  ray  of 
light  through  a  globule  of  water.  Let  SI  (Fig.  113.)  be  a  small 
beam  of  light  from  the  sun,  falling  upon  the  surface  of  a  globule  of 
water  at  I.  Agreeably  to  what  is  known  of  the  laws  of  light  in 
passing  out  of  one  transparent  medium  into  another,  a  portion  of  the 
rays  would  be  reflected  at  I,  and  another  portion  would  pass  into  the 
drop  and  be  refracted  to  the  farther  surface  at  Fig-  I13- 

F.     The  same  effect  would  recur  here,  and\s 
also  at  I",  and  at  \"  ;  and  were  the  eye  situa-    V 
ted  in  either  of  the  lines  PR',  I"R",  or  I'"R"',      \ 
it  wdilld  perceive  the  prismatic  colors,  because  JL^    \ 
some  of  the  rays  which  composed  the  beam  of 
light  that  reached  -the  eye,  would  be  refracted 
more  than  others  and  thus  the  different  colors 


THE    RAINBOW. 


287 


would  be  made  to  appear.  Or  if  a  screen  were  so  placed  as  to  re- 
ceive these  transmitted  rays,  a  faint  spectrum  would  be  formed  upon 
it.  Such  a  progress  of  a  beam  of  light  admitted  through  the  win- 
dow shutter,  and  made  to  fall  on  a  globular  vessel  of  water,  may  be 
actually  rendered  visible  by  experiment. 

514.  It  may  be  remarked  that  but  a  comparatively  small  part  of 
the  solar  rays  that  shine  upon  a  drop  of  water,  are  required  in  order 
to  produce  the  mild  light  of  the  rainbow,  aided  as  its  light  is  by  the 
dark  ground  or  cloud  on  which  it  is  usually  projected ;  yet  where 
the  number  of  rays  that  enter  the  eye  is  diminished  beyond  a  certain 
limit,  the  light  becomes  too  feeble  for  distinct  vision.  It  will  also  be 
observed,  that  a  considerable  portion  of  light  is  lost  at  each  success- 
ive reflexion  that  takes  place  within  the  drop,  so  that  a  certain  beam 
of  light,  conveyed  to  the  eye  after  two  reflexions,  will  be  much  more 
feeble  than  the  same  beam  after  one  reflexion.  Indeed,  so  much  of 
the  sun's  light  is  dissipated  at  the  first  point  of  reflexion  from  the  in- 
terior surface,  added  to  what  is  transmitted  at  the  same  point,  and  of 
course  never  reaches  the  eye  of  the  spectator,  that,  were  it  not  for  a 
great  accumulation  which  the  sun's  rays  undergo  at  a  particular  point 
in  this  drop,  whence  the  light  is  reflected  and  conveyed  to  the  eye, 
the  phenomena  of  the  rainbow  would  not  occur.  The  manner  in 
which  this  accumulation  is  effected,  is  now  to  be  explained. 


Fig.  114. 


515.  Let  fzpq 
(Fig.  114.)  be  the 
section  of  a  drop  of 
rain,  fp  a  diameter, 
a  &,  e  d,  &c.  parallel 
rays  of  the  sun's  light, 
falling  upon  the  drop, 
Now  yfj  a  ray  coin- 
ciding with  the  diam- 
eter, would  suffer  no 
refraction;  and  a 6,  a 
ray  near  to  yf,  would 
suffer  only  a  very 
small  inclination  to- 
wards the  radius,  so  as  to  meet  the  remoter  surface  of  the  drop  very 


288  OPTICS. 

near  to  p;  but  the  rays  which  lie  farther  from  yf,  being  inclined  to- 
wards the  radius  in  a  greater  angle,  would  be  more  and  more  re- 
fracted as  they  were  farther  removed  from  the  diameter.  The  con- 
sequence would  be,  that  after  passing  a  certain  limit,  the  rays  that  lay 
above  that  limit'  would  cross  those  which  lay  below  it  and  meet  the 
further  surface  somewhere  between  the  diameter  and  the  ray  which 
passed  through  the  said  limit;  that  is,  all  the  rays  falling  on  the  quad- 
rant/2, would  meet  the  circumference  within  the  arc  kp.  But  when 
a  quantity  is  approaching  its  limit,  or  is  beginning  to  deviate  from  it, 
its  variations  are  nearly  insensible.  Thus,  when  the  sun  is  at  the 
tropics,  being  the  limits  to  which  he  departs  from  the  equator,  he 
appears  for  some  lime  to  remain  at  the  same  point.  In  the  same 
manner,  a  great  number  of  the  rays  which  lie  contiguous  to  e  d,  on 
both  sides  of  it,  will  meet  in  very  nearly  the  same  point  on  the  con- 
cave surface  of  the  drop  at  Jem.  Consequently,  a  greater  number 
of  rays  will  be  reflected  from  that  point  than  from  any  other  in  the 
arc.  Moreover,  proceeding  from  a  single  point,  they  will  emerge 
parallel,  and  therefore  more  of  them  will  enter  an  eye  favorably 
situated,  than  if  they  passed  out  diverging.  On  both  these  accounts, 
it  appears,  that  there  is  a  particular  point  in  a  drop  of  rain,  where 
the  rays  of  the  sun's  light  seem  to  accumulate,  and  are  therefore  pe- 
culiarly fitted  to  make  an  impression  on  the  organ  of  vision.  It  is 
found  by  calculation  that  the  angle  which  the  incident  and  emergent 
rays,  in  such  cases,  make  with  each  other,  is,  for  the  red  rays  42°  2', 
and  for  the  violet  rays  40°  17'.  These  are  the  angles  when  the  rays 
emerge  after  two  refractions  and  one  reflexion :  in  the  case  of  two 
refractions  and  two  reflexions,  the  angles  are,  for  the  red  rays  50°  59', 
and  for  the  violet  54°  9'. 

516.  Let  us  next  consider  what  must  be  the  position  of  the  spec- 
tator in  order  that  his  eye  may  receive  the  emergent  rays  which 
make  the  foregoing  angle  with  the  incident  rays,  and  which  of 
course  are  those  which  cause  the  phenomena  of  the  rainbow. 

The  spectator  must  stand  with  his  back  to  the  sun,  and  a  line 
drawn  from  the  sun  towards  the  bow,  so  as  to  pass  through  his  eye, 
will  make  the  same  angle  with  the  emergent  rays  that  they  make  with 
the  incident  rays.  Thus,  let  AB  be  the  incident  and  GI  the  emer- 
gent ray,  and  let  the  angle  which  these  two  rays  make  with  each  other 


THE    RAINBOW 


289 


Fig.  115. 


be  AKI;  and  let  IT  be  a  ray  passing  from  the  sun  towards  the  bow 
through  the  eye  of  the  spectator ;  then,  (since  the  rays  of  the  sun 
may  be  regarded  as  parallel,)  AB  and  IT  are  parallel,  and  the  al- 
ternate angles  AKI  and  KIT,  equal.  But  AKI  is  the  angle  made 
by  the  incident  and  emergent  rays,  and  KIT  the  angle  made  by  the 
emergent  ray,  and  a  line  drawn  from  the  sun  towards  the  bow  through 
the  eye  of  the  spectator. 

517.  When  the  sun  shines  upon  the  drops  of  rain  as 'they  are  fall- 
ing, the  rays  which  come  from  those  drops  to  the  eye  of  the  spectator 
after  ONE  REFLEXION  AND  TWO  REFRACTIONS,  produce  the  inner- 
most or  primary  rainbow ;  and  those  rays  which  come  to  the  eye 
after  TWO  REFLEXIONS  AND  TWO  REFRACTIONS,  produce  the  outer" 
most  or  superior  rainbow. 


Let  SOC*  be  a  straight  line  passing 
from  the  center  of  the  sun  through  the 
eye  of  the  spectator  at  O  towards  the 
bow,  and  let  SR,  SV  be  incident  rays 
which  after  one  reflection  and  two  re- 
fractions are  conveyed  to  the  eye  at  Q, 
making  (Art.  516.)  with  SOC  angles 
equal  to  those  formed  by  the  incident 


Fig.  116. 


*  It  will  be  observed  that  the  line  SOC  is  at  right  angles  to  the  plane 
of  the  surface,  that  is,  to  the  plane  of  the  bows. 

37 


290  OPTICS. 

and  emergent  rays.  If  OV  makes  with  SOC  an  angle  of  40°  IT, 
and  be  conceived  to  revolve  around  OC,  describing  the  surface  of  a 
cone,  all  the  drops  of  rain  on  this  surface  will  be  precisely  in  the 
situation  necessary  in  order  that  the  violet  rays,  after  two  refractions 
and  one  reflexion,  may  emerge  parallel  and  arrive  at  the  eye  in  O, 
and  this  will  not  take  place  in  the  same  manner  on  any  other  part  of 
the  cloud ;  so  that  by  means  of  this  species  of  rays,  the  spectator 
will  see  on  the  cloud  a  violet  colored  arc,  of  which  OC  will  be  the 
axis,  and  C  the  center.  He  will  besides,  see  also  an  infinity  of  oth- 
er concentric  arcs  exterior  to  the  violet,  each  one  of  which  will  be 
made  up  of  a  single  species  of  rays ;  and  according  as  these  rays 
are  less  refrangible,  their  areas  will  be  of  greater  diameter,  so  that 
the  largest,  composed  of  the  extreme  red  will  subtend  an  angle  ROC 
of  42°  2'.  Therefore,  the  whole  width  of  the  colored  bow  will  be 
4£°2' —  40°  17',  or  1°  45',  the  red  being  on  the  outside  and  the 
violet  within. 

The  contrary  order  of  colors  will  result  from  two  reflexions  and 
two  refractions.  Let  SV,  SR/,  be  the  incident  rays,  which  after 
two  reflexions  and  two  refractions  are  converged  to  the  eye  at  O, 
making  (Art.  516.)  with  SOC  angles  equal  to  those  formed  by  the 
incident  and  emergent  rays,  namely,  50°  59'  and  54°  9',  and  the 
lines  RO7  and  VO',  as  before,  be  conceived  to  revolve  around  SOC; 
they  will  severally  meet  with  all  the  drops,  which  having  twice  re- 
fracted and  twice  reflected  the  extreme  red  and  violet  rays,  can 
transmit  them  to  the  eye  parallel  to  each  other.  Between  these  two 
arcs,  there  will  be  others  exhibiting  all  the  intermediate  prismatic 
colors;  and  the  whole  together  will  form  a  second  bow,  whose 
breadth  will  be  54°  9'  — 50°  59',  or  3°  10'. 

518.  The  rays,  therefore,  which  come  from  all  the  drops  which 
make  an  angle  of  42°  2'  with  a  line  passing  from  the  sun  through 
the  eye  (which  may  be  called  the  axis  of  vision)  appear  red  ;  and  it 
is  obvious  that  a  collection  of  rays  drawn  all  around  this  axis  from 
the  eye  to  drops  thus  situated  would  form  a  cone,  of  which  the  drops 
themselves  would  constitute  the  base,  and  of  course  would  form  a 
circle,  'fhe  same  is  true  of  all  the  other  colors  which  emerge  from 
drops  at  angles  which  are  different  for  different  colors  but  constant 
for  the  same  color.  Hence,  the  line  which  passes  from  the  sun 


COLORS    OF    BODIES. 


291 


through  the  eye  of  the  spectator,  passes  also  to  the  center  of  the  bow, 
or  is  the  axis  of  the  cone  of  which  the  bow  itself  is  the  base.  If 
the  sun  is  on  the  horizon,  this  axis  becomes  a  horizontal  line ;  con- 
sequently, the  center  of  the  arch  rests  on  the  opposite  horizon,  and 
the  bow  is  a  semi-circle,  of  which  the  highest  point  -has  an  altitude 
above  the  horizon  of  42°  2'.  If  the  sun  is  at  this  altitude  of  42°  2' 
above  the  horizon,  then  the  center  of  the  bow  will  have  the  same 
depression  below  the  opposite  horizon,  and  the  circumference,  at  its 
highest  point  will  just  reach  that  horizon.  When  the  sun  is  between 
these  two  points,  the  elevation  of  the  bow  will  be  the  difference  be- 
tween the  altitude  of  the  sun  and  the  foregoing  angle. 

519.  When  the  spectator  is  on  an  eminence,  as  a  high  mountain, 
he  may  see  more  than  half  the  bow,  when  the  sun  is  near  setting ; 
for  the  axis  will  in  that  case  pass  to  a  point  above  the  opposite  hori- 
zon.    Travellers  who  have  ascended  very  high  mountains,  have  oc- 
casionally observed  their  shadows  projected  on  the  clouds  below, 
with  their  heads  encircled  with  rainbows.     In  this  case,  the  axis  pass- 
es to  a  point  above  the  opposite  horizon  equal  to  or  greater  than  the 
semi-diameter  of  the  bow,  so  that  the  whole  of 'the  circumference 
comes  into  view ;  and  the  eye  of  the  spectator  being  in  the  axis, 
the  entire  bow  is  projected  around  that  as  a  center,   upon  the  sur- 
face of  the  clouds. 

Colors  of  Bodies. 

520.  According  to  the  Newtonian  theory,  the  color  of  a  body  de- 
pends on  the  kind  of  light  which  it  reflects.     A  great  number  of 
bodies  are  fitted  to  reflect  at  once  several  kinds  of  rays,   and  conse- 
quently appear  under  mixed  colors.     It  may  even  happen  that  of  two 
bodies  which  should  be  green,  for  example,  one  may  reflect  the  pure 
prismatic  green,  and  the  other  the  green  which  arises  from  the  mix- 
ture of  yellow  and  blue.     This  quality  of  selection  as  it  were  in 
bodies,  which  varies  to  infinity,  occasions  the  different  kinds  of  rays 
to  unite  in  every  possible  manner  and  every  possible  proportion ;  and 
hence  the  inexhaustible  variety  of  shades  which  nature  as  in  sport 
has  diffused  over  the  surfaces  of  different  bodies. 

When  a  body  absorbs  nearly  all  the  light  that  reaches  it,  that  body 
appears  black :  it  transmits  to  the  eye  so  few  reflected  rays,  that  it 


292  OPTICS. 

is  scarcely  perceptible  in  itself,  and  its  presence  and  form  make  no 
impression  on  us,  unless  as  it  interrupts,  in  a  manner,  the  brightness 
of  the  surrounding  space. 


CHAPTER  IV. 

OF  VISION. 

521.  As"  a  preparation  for  studying  the  optical  structure  of  the 
eye,  and  the  laws  of  vision,  it  will  be  useful  first  to  learn  in  what 
way  images  of  external  objects  are  formed  in  a  dark  room,  by  light 
admitted  through  a  hole  in  the  window  shutter. 

522.  Jl  beam  of  light  from  the  sun,  entering  into  a  dark  room 
through  a  small  orifice  and  striking  upon  an  opposite  wall  or  screen, 

forms  a  circular  image  on  the  wall,  whatever  be  the  shape  of  the  orifice. 

We  will  suppose  the  orifice  to  be  comparatively  large,  as  an  inch 
in  diameter,  and  of  a  triangular  or  of  an  irregular  shape ;  the  image 
formed  on  the  wall  will  still  be  circular.  For,  suppose  the  orifice  to 
be  reduced  to  a  very  small  circular  hole,  as  a  pin  hole,  (which  may 
easily  be  done  by  placing  over  the  orifice  a  metallic  plate,  as  a  sheet 
of  lead,  pierced  by  a  pin,)  then  the  rays  of  the  sun  passing  through 
this  small  opening  would  of  course  be  circular.  But  the  large  irreg- 
ular orifice  may  be  considered  as  made  up  of  such  smaller  apertures, 
or  the  metallic  plate  may  be  conceived  to  be  pierced  with  an  indefi- 
nite number  of  pin  holes,  and  the  entire  image  formed  upon  the  wall 
may  be  conceived  to  be  made  up  of  an  assemblage* of  all  these 
images  of  the  sun  blended  with  each  other,  and  therefore  as  bounded 
by  innumerable  curve  lines  composed  of  the 
individual  circles.  Fis- 117- 

If  the  screen  be  brought  near  to  the  ori- 
fice, however,  the  image  will  be  of  the  same 
figure  as- the  orifice;  for  the  rays  after  they 
have  passed  the  orifice,  must  have  diverged 
considerably  before  the  sections  that  form 
the  image  shall  afford  circles  so  large,  that 
their  blended  circumferences  shall  compose 
a  circular  figure.  (See  Fig.  117.) 


VISION.  293 

If  the  plane  which  receives  the  image,  be  not  parallel  to  the  orifice, 
then  the  image  will  be  elliptical,  being  the  section  of  a  cone  oblique 
to  its  axis. 

Circular  images  of  the  sun  are  sometimes  projected  on  the  ground, 
through  the  small  openings  among  the  leaves  of  trees.  During  an 
eclipse  of  the  sun,  these  images  copy  the  figure  of  the  eclipse. 

If  there  be  various  orifices  near  to  each  other,  three,  for  example, 
through  which  a  beam  of  the  sun  shines  into  a  dark  room,  we  shall 
observe  at  first,  at  a  certain  distance,  three  distinct  luminous  circles. 
At  a  greater  distance,  these  three  circles  begin  to  be  blended,  and 
finally,  on  enlarging  sufficiently,  they  unite  to  form  a  single  circle. 

523.  lft  instead  of  a  beam  of  solar  light,  we  admit  into  a  dark 
room,  through  an  opening  in  the  shutter,  the  light  reflected  from  va- 
rious objects  without,  an  inverted  picture  of  these  objects  will  be 
formed  on  the  opposite  wall. 

A  room  fitted  for  exhibiting  such  a  picture  is  called  a  Camera 
Obscura. 

From  what  has  been  before  explained,  it  will  be  readily  under- 
stood, that  from  every  point  in  the  object,  innumerable  rays  of  light 
proceed  and  fall  upon  the  window  shutter.  Of  these,  however,  none 
can  enter  the  aperture  except  such  as  are  very  near  to  each  other, 
all  others  diverging  too  far  to  enter  a  small  opening.  It  is  essential 
to  the  distinctness  of  the  picture  that  rays  which  proceed  from  every 
point  in  the  object,  should  be  collected  into  corresponding  points  in 
the  image,  and  should  exist  there  free  from  any  mixture  of  rays  from 
any  other  point ;  and  it  is  essential  to  the  brightness  of  the  picture, 
that  as  many  rays  as  possible  should  be  conveyed  from  each  point 
in  the  object  to  its  corresponding  point  in  the  image.  To  render  the 
picture  distinct,  therefore,  the  opening  in  the  window  shutter  must 
be  small,  else  the  pencils  of  rays  from  different  points  will  overlap 
each  other,  and  confuse  the  picture ;  but  as  the  orifice  is  diminished 
the  brightness  of  the  picture  is  impaired,  since,  in  this  case>  a  smaller 
number  of  rays  is  conveyed  from  the  object  to  the  image. 

These  modifications  of  the  picture  according  to  the  size  of  the 
aperture,  may  be  easily  exhibited  by  beginning  with  a  circular  aper- 
ture two  or  three  inches  in  diameter,  and  reducing  its  size  gradually 


294  OPTICS. 

by  covering  it  with  a  piece  of  board,  or  a  metallic  plate,  perforated 
with'  holes  of  different  sizes.* 

524.  If,  instead  of  passing  through  the  naked  orifice,  the  rays  be 
received  on  a  convex  lens,  an  inch  and  a  half  or  two  inches  in  diam- 
eter fixed  in  the  window  shutter,  a  very  bright  and  distinct  picture 
of  the  external  landscape  will  be  formed  on  a  screen,  placed  at  the 
focal  distance  of  the  lens. 

The  image  is  brighter  and  more  distinct  than  when  formed  with- 
out the  aid  of  the  lens,  first,  because  the  diameter  of  the  lens  may  be 
so  great  as  to  receive  and  transmit  a  much  larger  portion  of  the  rays 
which  proceed  from  each  point  of  the  object,  than  would  be  com- 
patible with  distinctness,  if  so  large  a  naked  aperture  were  employ- 
ed ;  secondly,  because  the  rays  of  each  pencil  are  brought  more  ac- 
curately to  a  separate  focus;  and,  thirdly,  because,  the  picture  being 
formed  nearer  to  the  window  shutter,  it  is  smaller,  and  of  course  the 
light,  being  spread  over  less  space,  is  more  intense. 

A  convex  lens  fixed  in  a  ball,  is  used  for  this  purpose,  which  is  so 
attached  to  the  opening  in  the  shutter  as  to  be  capable  of  being  turn- 
ed towards  different  parts  of  the  landscape,  like  the  eye-ball  in  its 
socket.  Such  a  lens  with  its  accompanying  parts,  is  called  a  Sciop- 
tic  ball. 

In  a  bright  sunny  day,  where  the  sun  is  on  the  side  of  the  house 
opposite  to  the  shutter,  and  of  course  illuminating  the  sides  of  objects 
which  face  the  window,  we  may  form  either  with  or  without  the  aid 
of  the  scioptic  ball,  a  very  striking  and  beautiful  picture  of  external 


*  A  small  room,  ten  feet  square,  for  example,  having  a  window 
opening  towards  an  unobstructed  landscape,  may  easily  be  converted 
into  a  camera  obscura.  The  perforation  in  the  shutter,  must  be  made 
equidistant  from  the  sides  of  the  room:  and  from  the  aperture  as  a 
center,  with  a  radius  equal  to  the  distance  of  the  opposite  wall,  de- 
scribe an  arc  of  a  circle,  upon  which  as  a  base  a  new  concave  wall  is 
to  be  constructed,  finished  with  stucco.  The  other  walls  and  ceiling 
are  to  be  Colored  a  dead  black,  while  the  concave  wall,  for  receiving 
the  image,  is  made  as  white  as  possible.  On  admitting  the  light 
through  an  aperture  half  an  inch  in  diameter,  a  beautiful  and  distinct 
picture  will  be  formed  on  the  opposite  wall. 


VISION.  295 

objects,  exhibiting  each  in  its  relative  situation,  of  a  size  and  bright- 
ness corresponding  to  its  distance,  with  all  the  colors  and  the  most 
delicate  motions  of  the  landscape.  The  name  camera  obscura,  which 
appropriately  belongs  to  such  a  chamber,  is  also  extended  to  certain 
boxes  in  which  similar  pictures  are  formed,  with  peculiar  devices  for 
rendering  the  image  erect  instead  of  inverted.  The  structure  of 
these  portable  camera  obscuras,  may  be  described  more  particularly 
among  other  optical  instruments. 

The  eye  is  a  camera  obscura,  and  the  analogy  existing  between 
its  principal  parts,  and  the  contrivances  employed  to  form  a  picture 
of  external  objects  as  in  the  preceding  experiments,  will  appear  very 
striking  on  comparison. 

525.  The  EYE  consists  of  three  prin-  Fig.  us. 

cipal  chambers,  rilled  with  media  of  per- 
fect transparency.  The  first  of  these 
media,  A,  occupying  the  anterior  cham- 
ber, is  called  the  Aqueous  Humor,  and 
consists  chiefly  of  pure  water.  The  cell 
in  which  the  aqueous  humor  is  contain- 
ed, is  bounded,  on  its  anterior  side,  by  a 
strong,  horny,  and  delicately  transparent 
coat,  aa,  and  is  called  the  cornea. 

The  posterior  surface  of  the  chamber  A  of  the  aqueous  humor  is 
limited  by  the  Iris  cc,  which  is  a  kind  of  circular  opake  screen,  con- 
sisting of  muscular  fibres,  by  whose  contraction  or  expansion,  an 
aperture  in  its  center  called  the  pupil  is  diminished  or  dilated  ac- 
cording to  the  intensity  of  the  light.  In  very  strong  lights,  the  open- 
ing of  the  pupil  is  greatly  contracted,  so  as  not  to  exceed  twelve 
hundredths  of  an  inch  in  the  human  eye,  while  in  feebler  illumina- 
tions it  dilates  to  an  opening  not  exceeding  twenty  five  hundredths 
or  double  its  former  diameter.  The  use  of  this  is  evidently  to  mod- 
erate and  equalize  the  illumination  of  the  image  on  the  retina,  which 
might  otherwise  injure  its  sensibility.  In  animals,  as  the  cat,  which 
see  well  in  the  dark,  the  pupil  is  almost  totally  closed  in  the  day 
time,  and  reduced  to  a  very  narrow  line ;  but  in  the  human  eye, 
the  form  of  the  aperture  is  always  circular.  The  contraction  of  the 
pupil  is  involuntary,  and  takes  place  by  the  effect  of  the  stimulus  of 
the  light  itself;  a  beautiful  piece  of  self-adjusting  mechanism,  the 


296 


OPTICS. 


play  of  which  may  be  easily  seen  by  bringing  a  candle  near  to  the 
eye,  while  directed  to  its  own  image  in  a  looking  glass.  Immediate- 
ly behind  the  opening  of  the  Iris,  lies  the  Crystalline  Lens,  B,  en- 
closed in  its  capsule,  which  forms  the  posterior  boundary  of  the 
chamber  A.  The  figure  of  the  crystalline  lens  is  a  solid  of  revolu- 
tion, having  its  anterior  surface  much  less  curved  than  the  posterior. 
The  consistence  of  the  crystalline  is  that  of  a  hard  jelly,  and  it  is  pur- 
er and  more  transparent  than  the  finest  rock  crystal. 

In  the  crystalline  a  very  curious  and  remarkable  contrivance  is 
adopted,  for  overcoming  or  preventing  the  spherical  aberration  which 
(Art.  503.)  belongs  to  lenses  of  this  form,  which  refract  the  rays 
more  towards  their  marginal  than  near  their  central  parts,  and  hence 
do  not  bring  all  the  rays  belonging  to  one  pencil  to  the  same  focus. 
Here  the  difficulty  is  obviated  by  giving  to  the  central  portions  of  the 
crystalline  a  proportionately  greater  density,  thus  increasing  its  refract- 
ive power  so  as  exactly  to  correspond  to  that  of  the  other  portions  of 
the  lens. 

The  posterior  chamber  C  of  the  eye  is  filled  with  the  Vitreous 
Humor.  Its  name  is  derived  from  its  supposed  resemblance  to 
melted  glass ;  it  is  a  clear,  gelatinous  fluid,  very  much  resembling 
the  white  of  an  egg.  Rays  of  light  diverging  from  various  objects 
without,  on  passing  through  the  aqueous  humor,  (which  is  a  concavo- 
convex  lens)  have  their  divergency  much  diminished,  or  even,  in 
most  cases  are  rendered  converging^  and  in  this  state  are  transmitted 
through  the  crystalline,  which  has  precisely  such  a  degree  of  refract- 
ive power  as  enables  it  to  bring  them  to  a  focus  at  the  distance  of  the 
retina,  which,  as  a  screen,  is  spread  out  to  receive  the  image.  The 
retina  as  its  name  imports,  is  a  kind  of  white  net-work,  like  gauze 
formed  of  inconceivably  delicate  nerves,  all  branching  from  one  great 
nerve  O,  called  the  optic  nerve,  which  enters  the  eye  obliquely  at  the 
inner  side  of  the  orbit,  next  the  nose.  The  retina  lines  the  whole 
of  the  cavity  C  up  to  ii,  where  the  capsule  of  the  crystalline  com- 
mences. Its  nerves  are  in  contact  with,  or  immersed  in,  the  pigmen- 
tum  nigrum,  a  very  black  velvety  matter,  which  covers  the  choroid 
membranfy  mm,  and  whose  office  is  to  absorb  and  stifle  all  the  light 
which  enters  the  eye'  as  soon  as  it  has  done  its  office  of  exciting  the 
retina ;  thus  preventing  internal  reflexions,  and  consequent  confusion 
of  vision.  The  whole  of  these  humors  and  membranes  are  contain- 


VISION,  297 

ed  in  a' thick  tough  coat,  called  the  sderotica,  which  unites  with  the 
cornea  and  forms  what  is  called  the  white  of  the  eye. 

526.  Such  in  general,  is  the  structure  by  which  parallel  rays,  and 
those  coming  from  very  distant  objects  are  brought  to  a  focus  on  the 
retina.     But  there  are  special  contrivances,  suited  to  particular  pur- 
poses, which  are  no  less  evincive  of  design  and  skill  than  the  gener- 
al organization  of  the  eye.     Some  of  the  most  remarkable  of  these 
we  proceed  to  mention.     The  cornea,  by  protruding,  collects  the 
rays  of  light  that  come  to  the  eye  laterally,  and  guides  them  into  the 
eye,  thus  enlarging  the  range  of  vision.     It  answers  to  an  appendage 
to  the  microscope,  which  will  hereafter  be  described  under  the  name 
of  field  glass.     The  motion  of  the  eye-ball,  by  means  of  which  the 
pupil  may  be  turned  in  different  directions,  conduces  to  the  same 
purpose.     Hence,  notwithstanding  the  minuteness  of  the  aperture 
which  admits  the  light  (and  it  must  be  small,  otherwise  the  image 
will  not  be  distinct)  the  eye  may  take  in  at  once,  without  moving  the 
head,  a  horizontal  range  of  110°  and  a  vertical  range  of  120°,  name- 
ly, 50°  above,  and  70°  below  a  horizontal  line. 

527.  As  the  radiant  approaches  the  lens,    the  image  recedes 
from  it  on  the  other  side;  (see  Fig.  108;)  and  in  our  experiments 
on  the  formation  of  images  we  are  obliged  either  to  change  the 
place  of  the  screen  every  time  the  distance  of  the  radiant  is  altered, 
or  to  substitute  a  new  lens,  which  will  either  throw  back  the  image 
as  much  as  the  increased  distance  of  the  radiant  brings  it  forward, 
or  which  brings  the  image  as  much  nearer  as  the  altered  place  of  the 
radiant  tends  to  carry  it  off.     How  then  is  the  distinctness  of  the  im- 
age maintained  in  the  eye,  notwithstanding  the  immense  variety  in  the 
distances  of  objects  ?     We  can  conceive  of  but  two  ways  in  which 
this  can  be  accomplished :  either  by  lengthening  or  shortening  the 
diameter  of  the  eye  in  the  direction  of  its  axis,  so  as  to  alter  the  dis- 
tance of  the  retina  from  the  cornea  and  crystalline,  or  by  altering 
the  curvature  of  the  refracting  lenses  themselves,  increasing  their 
convexity  for  near  objects,  and  lessening  it  for  objects  that  are  more 
remote.     Perhaps  both  causes  may  operate,  but  the  effect  is  believed 
to  be  produced  chiefly  by  the  latter  cause,  namely,  change  of  figure 
in  the  refracting  lenses.     On  this  subject,  Sir  J.  Herschel  remarks, 

38 


298  OPTICS. 

that  it  is  the  boast  of  science  to  have  been  able  to  trace  so  far  the  re- 
fined contrivances  of  this  most  admirable  organ  ;  not  its  shame  to  find 
something  still  concealed  from  its  scrutiny ;  for,  however  anatomists 
may  differ  on  points  of  structure,  or  physiologists  dispute  on  modes 
of  action,  there  is  that  in  what  we  do  understand  of  the  formation  of 
the  eye  so  similar,  and  yet  so  infinitely  superior,  to  a  product  of  hu- 
man ingenuity, — such  thought,  such  care,  such  refinement,  such' ad- 
vantage taken  of  the  properties  of  natural  agents  used  as  mere  in- 
struments, for  accomplishing  a  given  end,  as  force  upon  us  a  convic- 
tion of  deliberate  choice  and  premeditated  design,  more  strongly, 
perhaps,  than  any  single  contrivance  to  be  found,  whether  in  art  or 
nature,  and  render  its  study  an  object  of  the  deepest  interest. 

528.  Writers  on  comparative  anatomy  express  the  highest  admi- 
ration of  the  adaptation  of  the  eyes  of  different  animals  to  the  media 
in  which  they  respectively  live,  and  to  the  peculiar  wants  or  habits  of 
each.  Thus  the  crystalline  lens  of  the  fish  is  formed  with  peculiar 
reference  to  the  refracting  properties  of  water.  In  the  human  eye, 
this  lens  has  a  refractive  power  only  a  little  greater  than  that  of  water ; 
but  since  the  light  passes  out  of  a  much  rarer  medium,  (air,)  such  a 
density  is  sufficient  to  bring  the  rays  to  a  focus ;  but  were  the  density 
of  the  crystalline  lens  in  the  eye  of  the  fish  no  greater  than  in  the 
human  eye,  receiving  the  light  from  a  medium  (water)  almost  as 
dense  as  itself,  it  would  be  unable  to  give  that  change  of  direction  to 
the  rays  which  would  be  essential  to  distinct  vision.  But  provision 
is  made  for  this  exigency  by  giving  to  the  crystalline  lens  a  much 
greater  density,  and  of  course  a  higher  refracting  power,  which  ena- 
bles it  completely  to  fulfil  its  purpose. 

Animals  which  have  occasion  to  see  in  the  dark,  as  the  owl  and 
the  cat,  have  the  power  of  opening  or  closing  the  pupil  to  a  much 
greater  extent  than  man.  By  this  means,  they  are  enabled  in  the 
dark  to  collect  a  far  greater  number  of  rays  of  light.  But  as  such 
an  expansion  of  the  pupil  would,  in  broad  day  light,  endanger  the 
safety  of  eyes  of  such  peculiar  delicacy,  the  iris  closes  over  the 
aperture  and  diminishes  it  with  every  increase  in  the  intensity  of  the 
light,  a  change  which  is  involuntary  on  the  part  of  the  animal.  In 
animals,  as  birds,  which  pounce  upon  their  prey,  the  pupil  of  the 
eye  is  elongated  perpendicnlarly,  while  in  those  that  ruminate,  as  the 


VISION.  299 

ox,  it  is  elongated  horizontally ;  being  in  each  case,  exactly  adapted 
to  the  circumstances  of  the  animal. 

529.  The  images  of  external  objects  are  of  course  formed  invert- 
ed on  the  retina,  and  may  be  seen  there  by  dissecting  off  the  posterior 
coats  of  the  eye  of  a  newly  killed  animal,  as  an  ox,  and  exposing 
the  retina  and  choroid  membrane  from  behind,  like  the  image  on  a 
transparent  screen,  seen  from  behind.  The  appearance  is  particu- 
larly striking  and  beautiful  when  the  eye  is  fixed  like  the  scioptic 
ball,  in  the  window  shutter  of  a  dark  room.  It  is  this  image,  and 
this  only,  which  is  felt  by  the  nerves  of  the  retina,  on  which  the  rays 
of  light  act  as  a  stimulus ;  and  the  impressions  therein  produced  are 
thence  conveyed  along  the  optic  nerve  to  the  sensorium,  in  a  man- 
ner which  we  must  rank  at  present  among  the  profounder  mysteries 
of  physiology,  but  which  appear  to  differ  in  no  respect  from  that  in 
which  the  impressions  of  the  other  senses  are  transmitted.  Thus,  a 
paralysis  of  the  optic  nerve  produces,  while  it  lasts,  total  blindness, 
though  the  eye  remains  open,  and  the  lenses  retain  their  transparen- 
cy ;  and  some  very  curious  cases  of  half  blindness  have  been  suc- 
cessfully referred  to  an  affection  of  one  of  the  nerves  without  the 
other.  On  the  other  hand,  while  the  nerves  retain  their  sensibility, 
the  degree  of  perfection  of  vision  is  exactly  commensurate  to  that  of 
the  image  formed  on  the  retina.  In  cases  of  cataract,  when  the 
crystalline  lens  loses  its  transparency,  the  light  is  prevented  from 
reaching  the  retina,  or  from  reaching  it  in  a  proper  state  of  regular 
concentration ;  being  stopped,  confused  and  scattered,  by  the  opake 
or  semi-opake  portions  it  encounters  in  its  passage.  The  image,  in 
consequence,  is  either  altogether  obliterated,  or  rendered  dim  and 
indistinct.  If  the  opake  lens  be  extracted,  the  full  perception  of 
light  returns ;  but  one  principal  instrument  for  producing  the  conver- 
gence of  the  rays  being  removed,  the  image,  instead  of  being  form- 
ed OTi  the  retina,  is  formed  considerably  behind  it,  and  the  rays  being 
received  on  it  in  a  state  of  convergence,  before  they  are  brought  to  a 
focus,  produce  no  regular  picture,  and  therefore  no  distinct  vision. 
But  if  we  give  to  the  rays  before  they  enter  the  eye,  a  certain  degree 
of  divergence,  as  the  application  of  a  convex  lens,  so  as  to  render 
the  lenses  of  the  eye  capable  of  finally  effecting  the  exact  conver- 
gence of  the  rays  upon^the  retina,  distinct  vision  is  the  immediate  r«- 


300  OPTICS. 

suit.  This  is  the  reason  why'persons  who  have  undergone  the  ope- 
ration for  the  cataract,  (which  consists  either  in  totally  removing,  or 
in  putting  out  of  the  way,  the  opake  crystalline,)  wear  spectacles  unu- 
sually convex.  Such  glasses  perform  the  office  of  an  artificial  crystal- 
line. An  imperfection  of  vision  similar  to  that  produced  by  the  re- 
moval of  the  crystalline,  is  the  ordinary  effect  of  old  age,  and  its 
remedy  is  the  same.  In  aged  persons,  the  cornea  loses  something 
of  its  convexity,  or  becomes  flatter.  The  refracting  power  of  the 
eye  is  by  this  means  diminished,  and  a  perfect  image  can  no  longer 
be  formed  on  the  retina,  the  point  to  which  the  converging  rays  tend 
being  beyond  the  retina.  The  deficient  power  is  supplied  by  a  con- 
vex lens,  in  a  pair  of  spectacles,  which  are  so  selected  and  adapted 
to  the  eye,  as  exactly  to  compensate  for  the  want  of  refracting  power 
in  the  eye  itself,  and  thus  the  rays  are  brought  to  a  focus  at  the  reti- 
na, where  alone  a  distinct  image  can  be  formed. 

530.  Short  sighted  persons  have  their  eyes  too  convex,  forming 
the  image  too  soon,  or  before  they  reach  the  retina.     Concave  glass- 
es counteract  this  effect.     Rare  cases  have  occured  where  the  cor- 
nea was  so  very  prominent  as  to  render  it  impossible  to   apply  con- 
veniently a  lens  sufficiently  concave  to  counteract  its  action.     Such 
cases  would  be  accompanied  with  immediate  blindness,  but  for  that 
happy  boldness  justifiable  only  by  the  certainty  of  our  knowledge  of 
the  true  nature  and  laws  of  vision,  which  in  such  a  case  has  suggest- 
ed the  opening  of  the  eye  and  removal  of  the  crystalline  lens,  though 
in  a  perfectly  sound  state.     Other  defects  of  eye  sight,  whose  cause 
has  been  ascertained  to  depend  on  mal-conformation  of  the  cornea, 
or  some  other  part  of  the  eye,  have  sometimes  been  remedied  by 
adapting  to  them  glasses  of  a  peculiar  construction,  possessing  optic- 
tal  properties  adapted  to  the  particular  defects  they  were  required  to 
remedy. 

531.  The  estimation  of  the  DISTANCES   and  MAGNITUDES  of  ob- 
jects is  not  dependent  on  optical  principles  alone,  but  the  information 
afforded  by  the  eye,  is  taken  in  connexion  with  various  circumstances 
that  influence  the  mind  in  judging  of  these  particulars. 

In  the  first  place  we  judge  of  the  distance  of  an  object  by  the  in- 
clination of  the  optic  axes,  which  is  greater  for  nearer  objects  and 


VISION.  301 

less  for  objects  more  remote.  But  beyond  a  certain  distance,  this 
method  is  very  indeterminate,  since  great  intervals  among  remote 
objects  would  scarcely  affect  the  inclination  of  these  axes.  In  the 
second  place,  we  judge  of  distance  by  the  apparent  magnitude  of 
known  objects ;  as  when  a  ship  of  large  size,  or  a  high  mountain, 
appears  comparatively  small,  we  refer  it  to  a  great  distance.  We 
are  also  frequently  deceived  in  our  estimate  of  distance  when  we  are 
approaching  large  objects,  as  a  great  city,  or  a  lofty  mountain :  we 
fancy  they  are  nearer  than  they  actually  are.  In  the  third  place,  we 
estimate  the  distance  of  objects  by  the  degree  of  distinctness  of  the 
parts,  or  brightness  of  the  colors.  Thus  a  smoky  mountain  is  refer- 
ed  to  a  great  distance  ;*  a  mountain  whose  sides  are  precipitous  and 
bare  (especially  where  the  rocks  have  a  new  and  fresh  appearance 
in  consequence  of  having  been  quarried  for  use)  appears  nearer  than 
the  reality  :  vessels,  or  steam  boats,  seen  through  a  mist  in  the  night 
have  sometimes  run  foul  of  each  other,  being  supposed  by  the  pilots 
to  be  much  farther  off,  in  consequence  of  the  indistinctness  of  their 
appearance.  In  the  fourth  place,  our  estimate  of  distance  is  affec- 
ted by  the  number  of  intervening  objects.  Hence,  distances  upon 
uneven  ground  do  not  appear  so  great  as  upon  a  plain ;  for  the  val- 
leys, rivers  and  other  objects  that  lie  low  are  many  of  them  lost  to 
the  sight.  On  this  principle,  the  breadth  of  a  river  appears  less 
when  viewed  from  one  side  than  from  the  center ;  a  ship  appears 
nearer  than  the  truth  to  one  unaccustomed  to  judge  of  distances  on 
the  water ;  and  the  horizontal  distance  of  the  sky  appears  much  great- 
er than  the  vertical  distance,  whence  the  aerial  vault  does  not  pre- 
sent the  appearance  of  a  hollow  hemisphere,  but  of  such  a  hemisphere 
much  flattened  in  the  zenith,  and  spread  out  at  the  horizon. 

532.  A  similar  variety  of  circumstances  affects  our  estimate  of 
the  magnitudes  of  bodies  seen  at  different  distances.  First,  the  vis- 
ual angle,  that  is,  the  angle  subtended  by  the  object  at  the  eye,  deter- 
mines the  size  of  objects  that  are  near  ;  but  it  is  scarcely  any  guide 
to  the  dimensions  of  remote  objects,  since  all  such  objects  subtend 


*  This  appearance  exhibits  the  true  color  of  the  atmosphere,  be- 
coming visible  in  consequence  of  the  extent  of  the  stratum,  and  the 
dark  ground  which  the  mountain  affords  upon  which  to  view  it. 


302  OPTICS. 

angles  at  the  eye  comparatively  very  small.  Thus,  on  this  principle 
a  fly  within  a  few  inches  of  the  eye  would  appear  larger  than  a  ship 
of  war  seen  at  some  distance  on  the  water.  A  giant  nine  feet  in 
height,  but  thirty  feet  off,  would  appear  no  larger  than  a  child  three  feet 
high  seen  at  the  distance  of  ten  feet.  But  as  this  result  is  not  con- 
formable to  experience,  it  is  evident  that  we  must  have  means  of 
judging  of  the  magnitudes  of  objects,  beside  that  derived  from  the 
visual  angle.  If  the  giant  were  to  remove  from  the  distance  of  ten 
feet  from  the  eye  to  that  of  thirty  feet,  his  image  on  the  retina  would 
be  only  one  third  as  long  as  before ;  but,  on  the  other  hand,  the  dis- 
tance is  trebled,  and  the  sort  of  combination  that  takes  place  in  us  of 
the  two  impressions,  the  one  of  magnitude  the  other  of  distance,  is 
like  the  constant  product  of  two  quantities,  of  which  one  increases  in 
the  same  ratio  as  the  other  diminishes  ;  whence  the  giant  would  ap- 
pear constantly  of  the  same  height,  at  whatever  distance  from  us  he 
was  seen. 

533.  This  corrected  result,  however,  we  can  make  only  in  cases 
when  we  are  familiar  with  the  actual  size  of  the  body.  When  not 
thus  familiar,  we  rely  too  much  on  the  visual  angle,  and  are  thus  of- 
ten greatly  deceived.  A  speck  on  the  window  being  at  the  instant, 
supposed  to  be  an  object  on  a  distant  eminence,  is  magnified,  in  our 
estimation  into  a  body  of  extraordinary  size  (as  a  line  half  an  inch  long 
into  a  may-pole) ;  or  distant  objects  supposed  to  be  very  near  appear 
of  an  exceedingly  diminutive  size.  Secondly,  the  effect  of  contrast 
is  visible  in  our  estimation  of  the  magnitudes  of  bodies,  a  given  ob- 
ject appearing  much  below  its  ordinary  size,  when  seen  by  the  side 
of  those  of  very  great  magnitude.  Men  quarrying  stone  at  the  base 
of  a  high  mountain,  sometimes  appear  at  a  little  distance  like  pig- 
mies, partly  from  the  effect  of  contrast,  but  more  perhaps  from  the 
impression  which  the  mountain  gives  us  of  their  being  nearer  than 
they  actually  are.  Thirdly,  objects  seen  at  an  angle  considerably 
above  or  below  us,  as  a  man  on  the  top  of  a  spire,  or  a  river  in  a 
deep  valley  seen  from  the  top  of  a  monntain,  appears  greatly  dimin- 
ished. In  these  cases,  since  there  are  no  intervening  objects  to  aid 
us  in  estimating  the  distance,  we  estimate  it  too  low,  and  hence  (Art. 
531.)  the  object  appears  less  than  the  reality.  Moreover,  being  seen 
obliquely,  its  apparent  dimensions  are  diminished  on  this  account,  the 


MICROSCOPES.  303 

apparent  diameter  being  determined  by  the  line  into  which  the  object 
is  projected  perpendicular  to  the  axis  of  vision.  Hence  children 
judge  much  less  accurately  both  of  distances  and  of  magnitudes  than 
adults,  and  blind  persons  suddenly  restored  to  sight  have  usually  dis- 
played an  utter  inability  to  judge  of  these  particulars. 


CHAPTER  V. 

OF  MICROSCOPES. 

534.  The  Microscope,  is  an  optical  instrument,  designed  to  aid 
the  eye  in  the  inspection  of  MINUTE  objects.* 

Telescopes,  on  the  other  hand,  assist  the  eye  in  the  examination 
of  distant  bodies.  These  two  instruments  have  probably  more  than 
any  other,  extended  the  boundaries  of  human  thought,  and  no  small 
part  of  the  labor  which  has  been  bestowed  upon  the  science  of  optics, 
has  had  for  its  ultimate  object  their  improvement  and  perfection. 

With  the  hope  of  making  the  learner  well  acquainted  with  the 
principles  of  the  microscope,  we  shall  begin  with  those  varieties  of 
the  instrument  which  are  the  most  simple  in  their  construction,  and 
successively  advance  to  others  of  a  more  complicated  structure. 

535.  The  simplest  microscope  is  a  double  convex  lens.     This,  it 
is  well  known,  when  applied  to  small  objects,  as  the  letters  of  a  book, 
renders  them  larger  and  more  distinct.     Let  us  see  in  what  manner 
these  effects  are  produced.     When  an  object  is  brought  nearer  and 
nearer  to  the  eye,  we  finally  reach  a  point  within  which  vision  begins 
to  grow  imperfect.     That  point  is  called  the  limit  of  distinct  vision. 
Its  distance  from  the  eye  varies  a  little  in  different  persons,  but  aver- 
ages (for  minute  objects)  at  about  five  inches.     If  the  object  be 
brought  nearer  than  this  distance,  the  rays  come  to  the  eye  too  di- 
verging for  the  lenses  of  the  eye  to  bring  them  to  a  focus  soon  enough, 
that  is,  so  as  to  make  the  image  fall  exactly  on  the  retina.     More- 
over, the  rays  which  proceed  from  the  extreme  parts  of  the  object 
meet  the  eye  too  obliquely  to  be  brought  to  the  same  focus  with 

*  fjuxpog,  small,  tfxotfg'w,  to  see. 


304  OPTICS. 

those  rays  which  meet  it  more  directly,  and  hence  contribute  only  to 
confuse  the  picture.  We  may  verify  these  remarks  by  bringing  grad- 
ually towards  the  eye  a  printed  page  with  small  letters.  When  the 
letters  are  within  two  or  three  inches  of  the  eye,  they  are  blended 
together,  and  nothing  is  seen  distinctly.  If  we  now  make  a  pin  hole 
through  a  piece  of  paper,  (black  paper  is  preferable,)  and  look  at 
the  same  letters  through  this,  we  find  them  rendered  far  more  distinct 
than  before  at  nearer  distances,  and  larger  than  ordinary.  Their 
greater  distinctness  is  owing  to  the  exclusion  of  those  oblique  rays 
which,  not  being  brought  by  the  eye  to  an  accurate  focus  with  the 
central  rays,  only  tend  to  confuse  the  picture  formed  by  the  latter. 
As  only  the  central  rays  of  each  pencil  can  enter  so  small  an  orifice, 
the  picture  is  made  up,  as  it  were,  of  the  axes  of  all  the  pencils. 
The  increased  magnitude  of  the  letters  is  owing  to  their  being  seen 
nearer  than  ordinary,  and  thus  under  a  greater  angle,  an  increase  of 
the  visual  angle  having  much  influence  in  our  estimate  of  the  magni- 
tude of  near  objects,  though  it  has  but  little  influence  in  regard  to 
remote  objects.  (Art.  532.) 

536.  A  convex  lens  acts  on  much  the  same  principles,  only  it  is 
still  more  effectual  It  does  not  exclude  the  oblique  rays,  but  it  di- 
minishes their  obliquity  so  much,  as  to  enable  the  eye  to  bring  them 
to  a  focus  at  the  distance  of  the  retina,  and  thus  makes  them  con- 
tribute to  the  brightness  of  the  picture.  The  object  is  magnified  as 
before,  because  it  is  seen  nearer,  and  consequently  under  a  larger  an- 
gle, which  enables  minute  portions  to  be  distinctly  recognized  by  the 
eye,  which  were  before  invisible,  because  they  did  not  occupy  a  suf- 
ficient space  on  the  retina.  The  power  of  a  lens  to  accomplish  these 
purposes,  will  obviously  depend  on  its  refractive  power;  and  this, 
(supposing  the  material  of  which  the  lens  is  made  to  remain  the 
same,)  will  depend  on  its  increased  sphericity,  and  diminished  focal 
distance.  Lenses  of  the  smallest  focal  distance,  therefore,  other 
things  being  equal,  have  the  greatest' magnify  ing  power,  and,  there- 
fore, spherules  or  perfect  spheres,  have  the  highest  magnifying  pow- 
ers G{  all.  When  the  radiant  is  situated  in  the  focus  of  a  lens,  the 
rays  go  out  parallel.  (Art.  501.)  When  thus  received  by  the  eye, 
they  are  capable  of  being  brought  to  a  focus  by  it,  and  of  forming  a 
distinct  image.  Hence,  by  means  of  a  lens,  an  object  may  be  seen 


MICROSCOPES. 


305 


distinctly  when  it  is  exceedingly  near  to  the  eye,  provided  it  be  situ- 
ated in  the  focus  of  the  lens.  The  magnifying  power  of  a  lens, 
therefore,  depends  on  the  ratio  between  its  focal  distance  and  the 
limit  of  distinct  vision.  The  latter  being  five  inches,  a  lens  whose 
focal  distance  is  one  inch,  by  bringing  the  object  five  times  nearer 
magnifies  its  linear  dimensions  in  the  same  ratio,  and  its  superficial 
dimensions  in  the  ratio  of  the  square.  Thus,  in  the  case  supposed, 
an  object  would  appear  five  times  as  long  and  broad,  and  have 
twenty  five  times  as  great  a  surface.  Lenses  have  been  made  ca- 
pable of  affording  a  distinct  image  of  very  minute  objects,  when 
their  focal  distances  were  only  ^\  of  an  inch.  In  this  case,  the 
magnifying  power  would  be  as  j\  :  5,  which  is  as  1  to  300,  or  as  1 
to  9000  in  surface. 

537.  When,  however,  an  object  is  so  near  to  the  eye,  a  very  minute 
space  covers  the  whole  field  of  vision,  and  it  is  only  the  minutest  ob- 
jects, or  the  smallest  parts  of  a  body,  that  are  visible  in  such  micro- 
scopes. The  extent  of  parts  seen  by  a  microscope  is  called  the 
field  of  view.  A  microscope  of  small  focal  distance  has  a  propor- 
tionally small  field  of  view.  Moreover,  since,  when  the  object  is  so 
near  to  the  lens,  the  rays  of  light  strike  the  lens  extremely  diverging, 
only  the  central  rays  of  each  pencil  can  be  brought  accurately  to  a 
focus.  The  more  oblique  rays,  therefore,  must  be  excluded  by  cov- 
ering up  all  but  the  central  portions  of  the  lens,  by  which  means  the 
brightness  of  the  image  is  diminished.  The  part  of  a  lens  through 
which  the  light  is  admitted,  is  called  its  aperture.  The  aperture  of  a 
lens  of  small  focal  distance  and  high  magnifying  powers,  must  of 
necessity  be  small,  and  one  of  the  principal  difficulties  in  the  use  of 
such  microscopes,  is  the  want  of  sufficient  light.  Hence,  micro- 
scopes of  different  focal  distances  are  required  for  different  purposes. 
Where  we  wish  to  view  a  large  object  at  once,  we  must  use  a  lens 
which  has  a  large  field  of  view,  and  of  course  but  comparatively 
small  magnifying  powers.  Such  are  the  glasses  used  by  watchma- 
kers and  other  artists.  Microscopes  which  magnify  but  little,  but 
afford  a  large  field  of  view,  are  called  magnifiers,  or  magnifying 
glasses.  Such  are  the  large  lenses  employed  for  viewing  pictures. 
But  for  inspecting  the  minute  parts  of  a  small  insect,  we  require  a 
much  higher  power ;  and,  the  object  being  very  small,  a  large  field 

39 


306  OPTICS. 

of  view  is  not  necessary.  The  only  difficulty  to  be  obviated  is  the 
want  of  light ;  and  this  evil  is  remedied,  either  by  placing  the  object 
in  the  sun,  or  by  condensing  upon  it  a  still  stronger  light,  by  means 
of  apparatus  specially  adapted  to  that  purpose,  which  will  be  de- 
scribed hereafter.* 

538.  Among  the  most  distinguished  achievements  of  philosophical 
artists,  in  our  own  limes,  has  been  the  formation  of  microscopes  out 
of  the  hardest  precious  gems,  especially  the  diamond  and  the  sap- 
phire. The  diamond  seems  to  unite  in  itself  almost  every  desirable 
quality  for  this  purpose.  It  will  be  recollected  that  this  substance  is 
distinguished  for  its  high  refractive  powers ;  hence,  a  given  refract- 
ing, and  of  course  magnifying,  power  may  be  attained  with  a  lens  of 
less  curvature,  and  consequently  subject  to  less  spherical  aberration, 
than  glass  lenses  of  the  same  power.  Indeed,  it  is  estimated,  that 
the  indistinctness  arising  from  spherical  aberration,  is  in  a  diamond 
lens  only  ^th  as  great  as  in  a  glass  lens  of  equivalent  power.  The 
sapphire  has  analogous  properties,  as  also  the  garnet;  and  pure  rock 
crystal  (quartz)  is  much  esteemed  for  refracting  lenses;  but  some  of 
the  pellucid  gems  are  unsuitable  for  this  purpose  on  account  of  their 
possessing  the  property  of  giving  double  images.  The  comparative 
curvatures  and  thicknesses  of  three  lenses  of  the  same  refracting 
power,  made  respectively  of  diamond,  sapphire,  and  glass,  are  ex- 
hibited in  the  following  diagrams. 

Fig.  119. 


Glass.  Sapphire.  Diamond. 

Since,  however,  a  diamond  lens  admits  of  being  made  much  thin- 
ner than  a  glass  lens  of  the  same  power,  the  loss  of  light  by  absorp- 
tion is  far  less  and  the  brightness  of  the  image  is  proportionally  aug- 
mented. 


*  A  convenient  pocket  microscope  is  sometimes  sold  in  the  shops, 
consisting  of  a  slide  of  ivory  or  horn,  two  or  three  inches  in  length, 
in  which  are  set  three  or  four  lenses  of  different  powers,  adapted  to    ' 
various  purposes. 


MICROSCOPES.  307 

539.  Another  distinguished  and  valuable  property  of  the  diamond 
is  that  it  combines  with  a  high  refractive,  a  low  dispersive  power. 
By  dispersive  power  it  will  be  observed,  is  meant  the  power  of 
separating  the  different  colored  rays,  that  is,,  of  decomposing  com- 
mon light   into  its  prismatic  elements.      Hence,   diamond   lenses 
are  naturally  nearly  achromatic,  or  afford  images  which  are  des- 
titute of  color.     But  while  these  favorable  qualities  were  known  to 
appertain  to  the  diamond,  which,  taken  in  connexion  with  its  great 
transparency  and  purity  of  structure,  were  observed  to  fit  it  admira- 
bly for  microscopes  of  great  magnifying  powers,  yet  the  extreme 
hardness  of  the  substance,  seemed  to  render  the  difficulty  of  grind- 
ing it  into  the  requisite  shape  almost  insuperable.     This  difficulty 
has,  however,  within  a  few  years,  been  completely  overcome  by  Mr. 
Pritchard,  an  eminent  English  artist,  who  has  constructed  a  number 
of  diamond  and  sapphire  microscopes,  whose  performances  have 
equalled  the  most  sanguine  expectations. 

540.  A  drop  of  a  transparent  liquor  may  be  easily  converted  into 
a  magnifier,  constituting  a  Fluid  Microscope.     The  simplest  kind  of 
fluid  microscope  is  formed  by  drilling  a  small  hole  in  a  plate  of  brass 
or  lead,  and  applying  to  it  a  drop  of  water  from  the  point  of  a  pin. 
If  the  plate  be  hollowed  out  on  both  sides  around  the  aperture,  the 
water  will  spontaneously  .assume  the  shape  of  a  convex  lens.     Water, 
however,  possessing  only  a  comparatively  low  refracting  power,  is 
less  adapted  to  this  purpose  than  several  other  fluids,  particularly 
certain  transparent  balsams  and  aromatic  oils.     Sulphuric  acid  and 
castor  oil  answer  well,  but  turpentine  varnish  and  Canada  balsam 
are  preferred,  especially  because  as  they  dry  they  become  indurated, 
and  form  permanent  microscopes.     Instead  of  the  aperture  in  a  me- 
tallic plate  above  described,  a  small  plate  of  glass  may  be  employed,  V 
in  which  case  it  is  only  necessary  to  drop  the  varnish  or  balsam  on  the 
surface  of  the  plate ;  and  it  will  assume  the  figure  of  a  plano-convex 
lens.     The  power  of  the  microscope  may  be  varied  by  employing 

a  larger  or  a  smaller  drop,  or  by  suffering  it  to  spread  itself  on  the 
upper  or  on  the  under  surface,  since  the  curvature  of  the  drop,  and 
of  course  its  focal  distance,  is  modified  by  each  of  these  circum- 
stances. 


308 


OPTICSc 


541.  The  PERSPECTIVE  GLASS,  which  is  used  for  viewing  pic- 
tures, affords  another  example  of  the  application  of  the  simple  mi- 
croscope. It  consists  of  a  large  double  convex  lens  fixed  in  a  frame 
in  a  vertical  position,  from  the  top  of  which,  on  the  back  side,  pro- 
ceeds a  plane  mirror  which  is  fixed  at  an  angle  of  45°  with  the  hori- 
zon, and  of  course  it  makes  the  same  angle  with  the  lens.  Pictures 
to  be  viewed  are  placed  in  an  inverted  position,  (that  is,  with  the 
top  towards  the  spectator,)  on  a  table  at  the  foot  of  the  instrument. 
The  mirror,  being  set  at  an  angle  of  45°  with  the  horizon,  renders 
horizontal  objects  erect.  (Art.  531.)  Its  office,  therefore,  is  merely 
to  give  a  proper  direction  to  the  rays  of  light  from  the  picture  as  they 
.enter  the  lens,  causing  them,  in  fact,  to  come  to  the  lens  in  the  same 
manner,  as  they  would  do  were  the  mirror  removed  and  the  picture 
set  up  in  a  vertical  position,  parallel  to  the  lens,  at  a  distance  from  the 
lens  equal  to  the  length  of  any  ray,  measured  from  the  picture  to 
the  mirror  and  from  the  mirror  to  the  lens.  (Art.  530.)  Again,  in 
order  that  the  image  may  be  erect,  it  is  necessary  that  the  picture 
should  be  placed  with  its  top  towards  the  observer ;  for  since  the 
image  of  every  point  in  the  picture  is  just  as  far  behind  the  mirror  as 
the  point  is  before  it,  those  parts  of  the  picture  which  are  designed 
to  occupy  the  highest  parts  of  the  image  must  be  farthest  below  the 
mirror.  This  will  be  understood  from  the  following  diagram. 

AA,  a  convex  lens  fixed  vertically 
in  a  frame. 

BB,  a  plane  mirror  making  with 
the  horizon  an  angle  of  45°. 

C,  an  object  placed  horizontally 
upon  the  table,  the  upper  part  being 
towards  the  observer. 

The  object  will  be  reflected  by  the 
mirror  into  a  perpendicular  position, 
and  its  rays  will,  therefore,  fall  on  the 
lens  in  the  same  manner  as  they  would 
were  it  actually  situated  perpendicu- 
larly, and  no  mirror  were  employed. 
Consequently,  if  the  distance  of  C 
from  the  lens  be  equal  to  die  focal  dis- 
tance of  the  lens,  the  rays  will  come 


MICROSCOPES. 

to  the  eye  parallel,  and  a  distinct  and  magnified  image  will  be  form- 
ed. If  the  distance  be  greater  than  the  focus  (as  it  may  be  ren- 
dered by  depressing  C  to  a  lower  level)  then  the  rays  will  come  to 
the  eye  converging,  and  the  image  will  be  more  magnified  but  less 
distinct.  If  the  distance  of  C  be  less  than  the  focus,  the  image  will 
be  less  magnified,  but  it  will  be  distinct  within  certain  limits.  The 
reasons  of  these  several  modifications,  will  be  evident  by  reflecting 
on  principles  already  expounded. 

When  the  glass  is  of  good  quality,  and  the  picture  executed  agree- 
ably to  the  rules  of  perspective,  the  various  parts  are  exhibited  in 
their  natural  positions,  and  at  their  relative  distances,  so  as  greatly  to 
improve  the  view.  The  greater  distinctness  of  the  parts,  and  more 
natural  distribution  of  light  and  shade  than  what  attends  the  naked 
view,  is  owing  not  only  to  the  increased  magnitude  and  to  the  great- 
er quantity  of  the  light  emitted  from  the  picture  which  is  collected 
by  the  lens  and  conveyed  to  the  eye,  but  also  to  the  separation  of 
this  portion  of  light  from  that  which  proceeds  from  various  other  ob- 
jects. The  lens  both  conveys  more  of  the  light  of  the  picture  to 
the  eye  than  would  otherwise  reach  it,  and  it  conveys  it  unmingled 
with  extraneous  light.  The  importance  of  the  latter  circumstance 
is  manifested  even  by  looking  at  the  picture  through  an  open  tube, 
or  through  the  hand  so  curved  as  to  form  a  tube. 

542.  The  microscopes  hitherto  examined  are  such  as  are  design- 
ed to  be  interposed  between  the  -eye  and  the  object  to  be  viewed, 
the  latter  being  placed  in  the  focus  of  parallel  rays  of  the  lens,  or  a 
little  nearer  to  the  lens  than  that  focus,  so  that  the  rays  of  the  same 
pencil  may  come  to  the  eye  either  parallel  or  with  so  small  a  degree 
of  divergency,  that  the  lenses  of  the  eye  shall  be  competent  to  make 
them  converge  and  form  an  image  on  the  retina.  In  this  case,  as 
the  rays  come  to  the  eye  in  the  same  manner  as  rays  from  larger 
objects,  at  a  greater  distance,  seen  without  the  aid  of  a  lens,  the  po- 
sition of  the  object  is  not  changed,  that  is,  it  is  seen  erect.  Single 
microscopes,  however,  are  also  employed  to  form  a  magnified  image 
on  a  wall  or  screen,  which  is  seen  by  the  eye  instead  of  the  object 
itself.  Two  celebrated  instruments,  the  Magic  Lantern  and  the  So- 
lar Microscope,  magnify  their  objects  in  this  manner,  in  the  construc- 
tion of  which  the  principles  under  review  are  happily  exemplified, 


310  OPTICS. 

543.  From  what  has  been  already  learned  respecting  lenses,  the 
following  points  will  be  readily  comprehended,  being  for  the  most  part 
a  recapitulation  of  principles  already  explained  and  demonstrated. 

If,  in  a  dark  room,  we  place  before  a  convex  lens  any  luminous 
object,  as  a  candle,  we  shall  observe  the  following  phenomena. 
(See  Art.  501.) 

1.  If  the  radiant  be  placed  nearer  to  the  lens  than  its  focus,  since 
the  rays  will  go  out  diverging,  no  image  will  be  formed  on  the  other 
side  of  the  lens. 

2.  Even  when  the  radiant  is  in  the  focus,  so  that  the  rays  go  out 
parallel,   they  never  meet  in  a  focus,  and  of  course  never  form  an 
image.* 

3.  But  when  the  radiant  is  farther  from  the  lens  than  its  focus,  the 
rays  converge  on  the  other  side,  those  of  each  pencil,  proceeding 
from  the  same  point  in  the  object,  being  accurately  united  in  one 
point  in  the  image,  and  occupying  that  point  alone,  without  the  inter- 
ference of  rays  from  any  other  point. 

4.  The  axes  of  the  rays  from  the  extreme  parts  of  the  object 
cross  each  other  in  the  center  of  the  lens.     Hence,  they  form  an 
image  inverted  with  respect  to  the  object;  and,  although  the  rays 
which  make  up  any  individual  pencil  are  made  to  converge  by  the 
lens,  yet  the  axes  (which  determine  the  magnitude  of  the  picture) 
diverge  from  each  other  after  crossing  at  the  center  of  the  lens,  and 
hence  the  image  is  greater  in  proportion  as  it  is  formed  at  a  greater 
distance  from  the  lens.     When  the  object  is  only  a  little  farther  off 
from  the  lens  than  its  focus,  the  image  is  thrown  to  a  great  distance, 
and  is  proportionally  magnified.     As  the  object  is  separated  farther 
from  the  lens  (which  may  be  effected  either  by  withdrawing  the  object 
from  the  lens  or  the  lens  from  the  object)  the  image  is  formed  at  a  less 
distance,  and  is  of  a  diameter  proportionally  less.    (See  Art.  502.) 
Suppose  now  that  we  employ  a  magnifier  of  so  small  focal  distance, 
that  when  the  object  is  placed  within  one  tenth  of  an  inch  of  the 
lens,  the  image  is  formed  on  the  other  side  upon  a  screen  or  wall  at 

*  If  will  be  remarked,  that  when  the  single  microscope  is  used  as 
an  eye  glass,  the  eye  itself  brings  the  parallel  rays  to  a  focus  and 
forms  the  image. 


MICROSCOPES.  311 

the  distance  of  twenty  feet ;  the  object  will  be  magnified  in  the  ratio 
of  TV  to  (20X12=)240;  that  is,  the  image  will  be  2,400  limes 
greater  than  the  object  in  diameter,  and  5,760,000  times  greater  in 
surface.  It  would  seem,  therefore,  as  if  nothing  more  were  neces- 
sary in  order  to  form  magnified  images  of  objects,  than  a  dark  room, 
a  convex  lens,  and  a  screen  or  wall  for  the  reception  of  the  picture. 
It  must  be  remarked,  however,  that  when  the  light  which  proceeds 
from  the  object  is  diffused  over  so  great  a  space,  its  intensity  must  be 
greatly  diminished,  so  as  to  be  either  incapable  of  affording  a  picture 
which  shall  be  visible  at  all,  or  at  least  sufficiently  bright  for  the  pur- 
poses of  distinct  vision.  This  difficulty  is  remedied  by  illuminating 
the  object ;  and  it  is  for  this  purpose,  that  most  of  the  contrivances 
employed  in  the  magic  lantern  and  solar  microscope  are  designed. 

544.  The  MAGIC  LANTERN  consists  of  a  large  tin  canister  either 
cylindrical  or  cubical  in  its  figure,  having  an  opening  near  the  bottom 
into  which  air  may  enter  freely  to  supply  the  lamp,  and  a  chimney 
proceeding  from  the  top  and  bent  over  so  as  to  prevent  the  light  of 
the  lamp  from  shining  into  the  room.  The  lantern  has  a  door  in  the 
side  which  shuts  close,  the  object  being  throughout  to  prevent  any 
light  from  escaping  into  the  room  except  what  attends  the  picture. 
The  room  itself  is  made  as  dark  as  possible ;  or,  what  is  better,  the 
experiments  are  performed  by  night.  In  front  of  the  lantern  is  fixed 
a  large  tube,  at  the  open  end  of  which  is  placed  the  magnifying  lens. 
In  the  same  tube,  at  a  distance  from  the  lens  somewhat  greater 
than  the  focal  distance,  the  object  is  introduced, -which  is  usually 
some  figure  painted  on  glass  in  transparent  colors,  the  other  parts  of 
the  glass  being  blackened  so  that  no  light  can  pass  through  except 
that  which  falls  on  the  object  and  illuminates  it,  by  which  means  we 
shall  have  a  luminous  image  projected  on  a  black  ground.  For  illu- 
minating the  object,  an  argand  lamp  is  placed  near  the  center  of  the 
lantern,  the  light  of  which  is  concentrated  upon  the  object  in  two 
ways ;  first,  by  means  of  a  thick  lens,  usually  plano-convex,  so  situ- 
ated between  the  lamp  and  the  object  that  the  rays  which  diverge 
from  the  lamp  shall  be  collected  and  condensed  upon  the  object ; 
and,  secondly,  by  means  of  a  concave  reflector  situated  behind  the 
lamp,  which  serves  a  similar  purpose. 


312 


OPTICS, 


A,  the  magnifying  Fig.  121. 
lens. 

B,  the  object,  in- 
troduced through  an 
qpening  in  the  tube. 

C,  the  condensing 
lens. 

D,  the  lamp. 

E,  the    concave 
mirror. 

F,  the  image  thrown  on  a  screen,  or  a  white"wall,  in  a  dark  room. 
a,  a  thumb-piece,  by  which  the  magnifier  may  be  made  to  approach 

or  to  recede  from  the  object,  and  thus  the  image  be  thrown  to  a 
greater  or  less  distance,  according  to  the  magnitude  required.  As 
the  image  is  inverted  with  respect  to  the  object,  it  is  only  necessary 
to  introduce  the  object  itself  in  an  inverted  position,  and  the  image 
will  be  erect. 

The  objects  employed  in  the  Magic  Lantern  are  very  various,  con- 
sisting of  figures  of  men  and  animals  ;  of  caricatures  ;  of  representa- 
tions of  the  passions  ;  of  landscapes  ;  and  of  astronomical  diagrams. 
When  the  last  are  employed,  this  apparatus  becomes  subservient  to  a 
useful  purpose  in  teaching  astronomy,  and  is  frequently  so  employed 
by  popular  lecturers  on  that  subject. 

545.  The  SOLAR  MICROSCOPE  does  not  differ  in  principle  from 
the  Magic  Lantern,  only  the  object  is  illuminated  by  the  concentra- 
ted light  of  the  sun  instead  of  that  of  a  lamp.  And  since  a  power- 
ful illumination  may  thus  be  effected  upon  minute  objects  placed  be- 
fore a'magnifier  of  great  power,  the  solar  microscope  is  usually  em- 
ployed to  form  very  enlarged  images  of  the  most  minute  substances, 
as  the  smallest  insects,  the  most  delicate  parts  of  plants,  and  other 
attenuated  objects  of  natural  history.  For  magnifiers,  several  of 
different  focal  distances  are  employed,  varying  from  an  inch  to  the 


T<T  or 


2o 


an  inch>  it  being  understood  that  those  of  the  short- 
est foc,us  and  greatest  magnifying  powers  can  be  used  only  for  the 
minutest  objects,  since,  when  bodies  of  a  larger  size  are  brought  so 
near  a  small  lens,  their  light  strikes  the  lens  too  obliquely  to  be  trans- 
mitted through  it.  The  magnifying  lens  is  fixed  into  the  mouth  of 


MICROSCOPES. 

a  tube  and  the  object  placed  near  its  focus,  much  in  the  same  man- 
ner as  in  the  magic  lantern ;  but  instead  of  the  body  of  the  lantern 
(which  contains  the  illuminating  apparatus)  a  mirror,  about  three  or 
four  inches  wide,  and  from  twelve  to  eighteen  inches  long,  is  attach- 
ed to  the  other  end  of  the  tube.  This  mirror  is  thrust  through  an 
opening  in  the  window  shutter  of  a  dark  room,  and  the  mouth  of  the 
tube  to  which  it  is  fixed  is  secured  firmly  to  the  shutter,  so  that  the 
mirror  is  on  the  outside,  and  the  tube  with  its  lenses  is  on  the  inside 
of  the  shutter.  By  means  of  adjusting  screws,  the  mirror  is  turned 
in  such  a  way  as  to  direct  the  sun's  rays  into  the  tube,  where  they  are 
received  by  one  or  more  of  the  lenses,  called  condensers,  which  col- 
lect them  and  concentrate  them  upon  the  object,  which  thus  becomes 
highly  illuminated,  and  capable  of  affording  an  image  sufficiently  bright 
and  distinct,  though  magnified  many  thousands  or  even  millions  of 
times.  It  will  be  observed  that  the  magnitude  of  the  image  depends 
here,  as  in  other  cases  of  the  simple  microscope,  upon  the  ratio  be- 
tween the  distances  of  the  object  and  the  image  from  the  center  of  the 
magnifier.  If,  for  example,  the  object  be  within  the  tenth  of  an  inch 
of  the  lens,  and  the  image  be  thirty  feet,  or  three  hundred  and  sixty 
inches  from  it,  then  the  image  will  be  3GO  X  10=3600  times  as  large 
as  the  object  in  diameter,  and  (3600)  2  =  12,960,000  times  in  sur- 
face. With  a  given  lens,  the  size  of  the  image  depends  wholly  on 
the  distance  to  which  it  is  thrown  ;  that  is,  on  the  distance  of  the  wall 
or  screen  where  it  is  formed. 

546.  When  the  solar  microscope  is  well  constructed,  it  affords  the 
most  wonderful  results,  and  greatly  enlarges  our  conceptions  of  the 
delicacy,  perfection,  and  subtility  of  the  works  of  nature.  In  in- 
specting vegetables,  the  eye  is  delighted  with  the  regularity  and 
beauty  which  characterizes  the  texture  and  intricate  structure  of 
plants  and  flowers.  The  most  delicate  fibres  of  a  leaf,  the  pores 
through  which  the  vegetable  fluids  circulate,  the  downy  covering  of 
plants,  and  foliage,  as  of  certain  mosses,  which  is  too  minute  to  dis- 
close its  figure  to  the  naked  eye,— objects  of  this  kind,  when  expand- 
ed under  the  solar  microscope,  astonish  and  delight  us  by  the  sym- 
metry of  their  structure.  Their  appropriate  colors  are  not  so  well 
exhibited  by  this  instrument,  as  by  some  other  forms  of  the  micro- 
scope to  be  described  hereafter.  In  the  animal  kingdom,  the  solar 

40 


314 


OPTICS. 


microscope  extends  the  range  of  vision  in  a  manner  no  less  surprising 
and  instructive.  The  minutest  insects  we  are  acquainted  with,  are 
exhibited  to  us  as  animals  of  the  largest  size,  and  often  of  monstrous 
shapes,  from  the  multiplicity  of  their  parts  and  apparent  dispropor- 
tion ;  and  animalcules,  or  those  members  of  the  animal  creation 
which  are  too  minute  to  be  seen  at  all  by  the  naked  eye,  are  sud- 
denly brought  into  life  in  countless  numbers.  The  forms,  the  mo- 
tions, and  the  habits  of  these  beings,  are  amorfg  the  most  curious 
revelations  of  the  solar  microscope.  The  circulation  of  the  blood 
may  be  seen  in  the  fins  of  fishes  and  other  transparent  parts  of  ani- 
mals, presenting  a  very  curious  and  interesting  spectacle.  The  crys- 
tallization of  salts,  which  may  be  exhibited  while  the  crystals  are 
forming  and  arranging  themselves,  (as  many  of  them  do  with  great 
precision  and  symmetry,)  is  among  the  finest  representations  of  this 
instrument. 

Since  the  light  is  transmitted  through  the  objects,  it  will  of  course 
be  understood,  that  only  such  objects  as  are  transparent  can  be  em- 
ployed in  the  manner  already  described.  In  some  varieties  of  the 
solar  microscope,  there  are  special  contrivances  for  exhibiting  opake 
objects  by  means  of  reflected  light. 

547.  If  we  form  an  image  of  an  object  with  the  single  microscope, 
(as  is  done  in  the  magic  lantern  and  solar  microscope,)  if  that  image 
is  not  too  large,  we  may  obviously  apply  to  it  a  magnifier  as  we  would 
to  an  original  object  of  the  same  size.  This  is  the  principle  of  the 
Compound  Microscope. 

The  COMPOUND  MICROSCOPE  consists  of  at 
least  two  convex  lenses,  one  of  which,  called 
the  olyect-glass,  is  used  to  form  an  enlarged 
image  of  the  object,  and  the  other,  called  the 
eye-glass,  is  used  to  magnify  the  image  still  far- 
ther. 

Thus,  let  ab  (Fig.  122.)  be  the  object,  being 
placed  a  little  farther  from  the  object  glass,  cd, 
than  the  principal  focus,  the  rays  of  light  ema- 
nating from  it  will  be  collected  on  the  other 
side  of  the  lens  and  form  an  image,  gh,  whose 
diameter  is  as  much  larger  than  that  of  the  ob- 
ject as  its  distance  from  the  lens  is  greater. 
(Art.  502.)  Let  ef  be  the  eye-glass,  which 


Fig.  122. 


MICROSCOPES. 


315 


must  be  placed  at  such  a  distance  from  the  image,  that  the  latter 
shall  be  in  the  focus  of  parallel  rays ;  then  the  rays  proceeding  from 
the  image  will  go  out  parallel,*  and  come  to  the  eye,  situated  behind 
the  glass,  in  a  state  favorable  for  distinct  vision. 

548.  The  magnifying  power  of  the  Compound  Microscope  is  es- 
timated as  follows.     First,  the  diameter  of  the  image  will  be  to  that 
of  the  object  as  their  respective  distances  from  the  lens.     Secondly, 
the  image  is  magnified  by  the  eye-glass  according  to  the  principles  of 
the  single  microscope,  (Art.  536.)  namely,  from  the  ratio  of  its  focal 
distance  to  the  limit  of  distincrvision.     Thus,  suppose  the  image  is 
formed  at  ten  times  the  distance  of  the  object ;  it  will  of  course  be 
magnified  ten  times.     Again,  suppose  the  eye-glass  has  a  focal  dis- 
tance of  one  inch,  the  limit  of  distinct  vision  being  five  inches ;  the 
image  will  be  farther  magnified  five  times;  by  both  glasses,  therefore, 
the  object  will  be  magnified  fifty  times.     If  the  first  ratio  be  that  of 
one  to  one  hundred,  then  the  instrument  will  magnify  the  linear  di- 
mensions five  hundred  times,  and  the  surface  two  thousand  five  hun- 
dred times.     From  this  double  magnifying  process,  it  might  be  sup- 
posed that,  by  means  of  the  compound  microscope,  it  would  be 
easy  to  attain  a  much  higher  magnifying  power  than  by  the  single 
microscope ;  but  this  is  not  the  fact ;  for,  in  the  first  place,  we  cannot 
form  an  image  of  a  size  beyond  certain  moderate  limits,  without 
making  it  too  large  for  the  eye-glass  to  cover ;  or,  if  an  eye-glass  of 
very  large  field  of  view  be  employed,  its  focal  distance  must  be  great, 
and  consequently  its  magnifying  power  small.     We  are,  therefore, 
unable  to  employ  so  high  a  magnifier  for  our  object-glass  as  we  may 
apply  to  the  naked  eye,  and  we  can  employ  only  a  microscope  of 
still  inferior  power  for  our  eye-glass. 

549.  On  account  of  the  necessity  of  using  a  large  eye-glass  to 
view  the  magnified  image,  compound  microscopes  require  to  have 
the  tube  which  contains  the  glasses,  larger  towards  the   eye-glass 
than  towards  the  object-glass.     Although  the  compound  does  not 

*  It  is  to  be  remarked  here  and  in  all  similar  cases,  that  it  is  only 
the  rays  of  each  individual  pencil  that  are  parallel ;  that  is,  those  rays 
which  come  from  the  same  point  in  the  object.  The  rays  of  differ- 
ent pencils  may  cross  each  other  variously,  and  the  different  pencils 
may  converge  or  diverge  among  themselves  ;  still  if  the  rays  of  each 
pencil  be  parallel  to  one  another,  the  vision  will  be  distinct. 


316 


OPTICS. 


possess  higher  magnifying  powers  than  the  simple  microscope,  yet  it 
commands  a  much  greater  field  of  view.  We  view  the  image  with 
the  eye-glass  in  the  same  manner  as  we  view  the  object  with  a  sin- 
gle microscope ;  but  having  already  a  magnified  representation  of 
the  object,  we  have  no  occasion  to  apply  to  the  eye  so  high  a  mag- 
nifier, and  therefore  we  may  employ  one  of  greater  focal  distance 
which  consequently  takes  in  a  greater  field  of  view.  The  field  of 
view  is  still  farther  improved  in  some  compound  microscopes  by  in- 
terposing a  field-glass,  which  is  a  convex  lens  introduced  between 
the  object-glass  and  the  place  of  the  image,  and  near  the  latter  (as 
a  little  below  gh9  Fig.  122,)  the  effect  of  which  is  to  diminish  the 
divergency  of  the  pencils  of  rays,  and  thus  to  bring  into  the  range 
of  the  eye-glass  those  pencils,  which  would  otherwise  diverge  too 
much  to  fall  within  it.  It  has  been  before  remarked  that  the  cornea 
performs  a  similar  office  for  the  crystalline  lens  of  the  eye.  (Art.  526.) 

550.  The  PORTABLE  CAMERA  OBSCURA,  which  is  used  chiefly 
for  delineating  landscapes,  consists  of  a  wooden  box,  (answering  to 
the  dark  chamber,  Art.  523.)  with  which  is  connected  a  convex  lens 
so  exposed  to  the  landscape  as  to  receive  the  rays  of  light  from  the 
various  objects  in  it,  and  form  a  picture  of  them  on  a  screen  placed 
within  the  box  at  the  focal  distance  of  the  lens.  Such  is  a  general 
description  of  the  instrument,  of  which  there  are  several  different 
forms.  The  following  diagram  represents  a  convenient  form. 

ABCD,  a  box  usually  made  of  thin  pie- 
ces of  mahogany. 

a  d,  a  plano-convex  lens,  this  form  being 
preferred  because  it  has  less  aberration  than 
a  double  convex. 

ED,  a  plane  mirror,  turning  on  a  hinge 
at  D,  and  capable  of  being  raised  or  low- 
ered, so  as  to  admit  more  or  less  of  the 
landscape. 

b  c,  a  piece  of  pasteboard,  covered  with 
a  sheet  pf  fine  white  paper  and  bent  a  so  as 
to  form  a  concave  screen,  and  placed  at 
the  focal  distance  of  the  lens.  A  casting 
of  stucco,  of  the  figure  of  a  concave  por-  A 
tion  of  a  sphere  affords  the  most  perfect  picture. 


Fig.  123. 


TELESCOPES. 


317 


The  rays  of  light  from  external  objects,  falling  upon  the  mirror 
ED  are  conveyed  to  the  lens  in  the  same  manner,  as  though  they 
came  directly  from  objects  at  the  same  distance  behind  the  mirror. 
Passing  through  the  lens,  they  are  brought  to  a  focus  and  form  a 
picture  of  the  landscape  on  the  screen,  which  may  be  viewed  by  an 
opening  in  'the  side  of  the  box  at  F,  and  may  be  copied  by  a  hand 
introduced  into  the  box  by  an  opening  below. 

Although  the  image  is  inverted  with  respect  to  the  objects,  yet  as 
the  spectator,  in  looking  into  the  box,  stands  with  his  back  to  the 
landscape,  the  picture  appears  erect. 


CHAPTER  VI. 

OF  TELESCOPES. 

551.  The  Telescope  is  an  optical  instrument,  designed  to  aid  the 
eye  in  viewing  distant  objects.* 

The  construction  of  this  noblest  of  instruments,  in  its  different 
forms,  involves  the  application  of  all  the  leading  principles  of  the 
science  of  Optics.  The  study  of  the  Telescope  is  therefore  the 
study  of  the  science,  and  a  distinct  enunciation  of  the  principles  in- 
volved in  it,  will  serve  as  a  recapitulation  of  the  most  useful  princi- 
ples of  Optics.  The  advantage  which  the  student  will  derive  from 
reviewing  these  points,  as  exemplified  in  their  application,  will  justify 
us  in  bringing  up  distinctly  to  view  various  principles  already  unfol- 
ded. 

552.  The  leading  principle  of  the  Telescope  may  be  thus  enun- 
ciated : 

By  means  of  either  a  convex  lens,  or  a  concave  mirror,  an  image 
of  the  object  is  formed,  which  is  viewed  and  magnified  with  a  micro- 
scope. 

The  most  general  division  of  the  instrument  is  into  Refracting  and 
Reflecting  Telescopes ;  of  which  the  former  produce  their  image  by 

*  ryjXs,  at  a  distance,  tfwjrsu,  to  see. 


318 


OPTICS. 


means  of  a  convex  lens,  and  the  latter  by  means  of  a  concave  mir- 
ror. The  instrument,  according  to  the  uses  to  which  it  is  applied, 
receives  the  farther  denominations  of  the  Astronomical  and  the  Ter- 
restrial Telescope  ;  and  also  Telescopes  are  named,  after  their  seve- 
ral inventors,  Galileo's,  Newton's,  Gregory's,  Herschel's,  &c. 

The  Astronomical  Telescope. 

553.  We  begin  with  this  variety  because  it  is  one  of  the  most  sim- 
ple, and  because  in  connexion  with  it,  we  may  conveniently  study  the 
theory  of  the  instrument  at  large. 

The  Astronomical  Telescope,  has  essentially  but  two  glasses :  these 
are  usually  fixed  in  a  tube  of  brass,  one  at  one  end,  and  the  other 
at  the  other  end.  The  glass  at  the  end  of  the  tube  which  is  directed 
to  the  object  is  called  the  object  glass,  and  that  at  the  end  to  which 
the  eye  is  applied,  is  called  the  eye  glass.  The  object  glass  is  a  con- 
vex lens  which  forms  an  image  of  a  distant  object,  as  a  star,  in  its  fo- 
cus of  parallel  rays,  and  the  eye-glass  is  a  microscope  with  which 
we  view  the  image,  at  a  distance  equal  to  its  focus  of  parallel  rays. 
Of  course,  the  distance  of  the  two  glasses  from  each  other  is  equal 
to  the  sum  of  thir  focal  distances.  See  the  annexed  figure. 


Fig.  124. 


MN,  object  glass. 
PQ,  eye  glass. 

A'D',  AD,  A"D",  parallel  rays  from  the  top  of  the  object. 
B'D',  BD,  B  'D",         "         "         "        center     ditto. 
C'D',  CD,  C"D",         "         "         "         bottom   ditto. 
6a,  inverted  image  formed  in  the  focus  of  parallel  rays. 
6PFr.  a  pencil  of  rays,  proceeding  from  the  top  of  the  image  to 
the  eye  glass  and  rendered  parallel. 
cKF,  a  similar  pencil  from  the  center. 
«QF,     ditto  the  bottom. 

F,  point  where  the  different  pencils  cross  the  axis. 


TELESCOPES. 


319 


554.  In  ibis  instrument  we  observe  a  striking  resemblance  to  the 
Compound  Microscope.  (Fig.    122.)     In  the  microscope,  however, 
since   the  object  is  nearer  than  the  image,  the  image  is  greater 
than  the  object ;  but  in  the  telescope,  since  the  object  is  removed  to 
a  great  distance,  the  image  is  formed  much  nearer  to  the  lens  than 
the  object,  and  is  proportionally  smaller.     Hence,  Compound  Mi- 
croscopes have  their  tubes  enlarged  in  diameter  towards  the  eye 
glass,  while  telescopes  have  their  tubes  diminished  in  that  direction. 
Since  the  vertical  angles  at  D,  subtended  on  the  one  side  by  the  ob- 
ject, and  on  the  other  by  the  image,  are  equal,  were  the  eye  situa- 
ted at  the  center  of  the  object  glass,  it  would  see  the  object  and  the 
image  under  the  same  visual  angle,  and  consequently,  both  would  ap- 
pear of  the  same  magnitude.     Moreover,  were  the  eye  placed  at  the 
same  distance  from  the  image  on  the  other  side  of  it,  it  would  be  ap- 
parently of  the  same  size  as  before  and  therefore  of  the  same  appa- 
rent diameter  as  the  object.     But  by  means  of  a  microscope,  such 
as  the  eye  glass  in  fact  is,  we  may  view  it  at  a  much  nearer  distance 
and  of  course  magnify  it  to  any  extent,  as  was  fully  shown  in  ex- 
plaining the  principles  of  the  simple  microscope.  (Art.  536.)     Hence 
the  magnifying  power  of  the  telescope  depends  on  the  ratio  between 
the  focal  distances  of  the  object  glass  and  the  eye  glass.     If,  as  in 
the  figure,  *the  common  focus  is  ten  times  nearer  the  eye  glass  than  to 
the  object  glass,  the  instrument  will  magnify  ten  times ;  if  one  hundred 
times  nearer,  one  hundred  times ;  and  so  in  all  other  cases.     Hence  we 
may  increase  the  magnifying  power  of  the  instrument,  either  by  em- 
ploying an  object  glass  of  very  small  curvature,  which  throws  its  im- 
age to  a  great  distance,  or  an  eye  glass  of  high  curvature  and  small  fo- 
cal distance.     Suppose  for  example,  the  object  glass  has  a  focal  dis- 
tance of  forty  feet,  or  four  hundred  and  eighty  inches,  and  the  eye 
glass  has  a  focal  distance  of  one  tenth  of  an  inch,  then  the  magnify- 
ing power  of  this  instrument  would  be  four  thousand  and  eight  hun- 
dred in  diameter,  and  the  square  of  this  number  in  surface. 

555.  As  the  sphericity  of  the  eye  glass  may  be  increased  indefi- 
nitely, and  its  focal  distance  diminished  to  the  same  extent,  it  would 
seem  possible  to  apply  very  high  magnifying  powers  in  very  short 
telescopes.     For  example,  suppose  the  focal  distance  of  the  object 
glass  is  twenty  four  inches ;  by  using  a  microscope  of  TV  of  an  inch 
focus,  we  have  a  power  of  two  hundred  and  forty.     But  it  must  be 


320  OPTICS. 

kept  in  mind,  that  such  microscopes  command  only  an  exceedingly 
small  field  of  view,  and  would,  therefore,  not  enable  us  to  see  any 
thing  more  than  a  minute  portion  of  an  object  of  any  considerable 
size ;  and  not  sufficient  light  would  be  transmitted  through  such  an 
aperture  toeanswer  the  purpose  of  vision. 

Since  the  image  is  inverted  with  respect  to  the  object,  and  is  view- 
ed in  this  situation  by  the  eye  glass,  objects  seen  through  Astronom- 
ical Telescopes  appear  inverted.  By  the  addition  of  several  more 
lenses,  they  may  be  made  to  appear  erect,  as  will  be  shown  in  the  de- 
scription of  the  Day  Glass,  or  Terrestrial  Telescope ;  but  at  every 
new  refraction  a  certain  portion  of  light  is  extinguished,  a  loss  which 
it  is  important  to  avoid  in  instruments  designed  to  be  used  at  night; 
while,  in  regard  to  celestial  objects,  it  is  not  essential  whether  they  are 
seen  erect  or  inverted.  The  place  for  the  eye  to  view  the  image  with 
the  best  advantage  is  at  F,  where  the  pencils  of  parallel  rays  meet. 

556.  The  difficulties  to  be  overcome  in  the  construction  of  a  per- 
fect Refracting  Telescope,  (some  of  which  are  very  formidable,)  are 
chiefly  the  following :    1.  Spherical  aberration;  2.  Chromatic  aber- 
ration ;  3.  Want  of  sufficient  light ;  4.  Want  of  a  field  of  view  suffi- 
ciently ample ;    5.  Imperfections  of  glass.     Each  of  these  particu- 
lars we  will  briefly  consider. 

557.  Spherical  aberration,  it  will  be  recollected,  occasions  indis- 
tinctness in  images  formed  by  lenses,  in  consequence  of  the  different 
rays  of  the  same  pencil  not  being  all  brought  to  a  focus  at  the  same 
point,  those  which  fall  upon  the  extreme  parts  of  the  lens  being  more 
refracted  and  coming  to  a  focus  sooner  than  those  which  are  nearer 
to  the  axis.    (See  Art.  503.)     The  amount  of  this  error  is  found  to 
depend  on  two  circumstances,  namely,  the  diameter  of  the  lens,  or 
what  is  technically  called  its  aperture,  and  its  focal  distance,  increas- 
ing rapidly  as  the  aperture  is  increased,  and  diminishing  as  the  focal 
distance  is  increased..    Small  apertures  and  flat  or  thin  lenses  are, 
therefore,  most  free  from  spherical  aberration.     But  if  we  use  small 
apertures  we  cannot  have  a  strong  light,  which  is  a  circumstance  of 
the  greatest  importance  in  astronomical  observations,  since  it  is  of 
little  consequence  to  enlarge  the  dimensions  of  an  object  if  we  have 
not  light  enough  to  render  it  visible.     Indeed,  many  astronomical 
objects,  as  small  stars,  are  rendered  visible  by  the  telescope,  not  in 
consequence  of  any  apparent  increase  of  size,  but  because  this  in- 


TELESCOPES. 


321 


strument  collects  and  conveys  to  the  eye  a  much  larger  beam  of 
light  from  them  than  would  otherwise  enter  it.  While  the  diameter 
of  the  beam  which  falls  upon  the  naked  eye  is  only  the  fraction  of 
an  inch,  that  collected  by  the  telescope  may  be  several  inches,  or 
even  several  feet,  according  to  the  size  of  the  instrument.  Hence, 
the  advantages  of  large  apertures  is  obvious.  Again,  we  cannot 
wholly  remedy  the  error  in  question,  though  we  may  diminish  it  by 
using  very  flat  lenses  which  have  great  focal  distances ;  but  the  ten- 
dency of  this  expedient  is  to  render  the  instrument  inconveniently 
long.  Other  expedients,  therefore,  become  necessary  for  correcting 
spherical  aberation  in  refracting  telescopes. 

558.  In  the  eye  glasses,  which  are  liable  to  the  same  difficulty, 
where  the  lens  has  a  great  curvature,  as  is  the  case  with  such  as  have 
high  magnifying  powers,  the  aperture  is  necessarily  reduced  very 
much,  by  excluding  all  the  light  except  what  passes  through  the  cen- 
tral parts  of  the  lens.  At  least  this  is  the  case  where  glass  lenses 
are  used.  'But  the  microscopes  made  of  diamond,  sapphire,  and 
other  gems,  have  not  only  high  refractive  powers,  but  are  less  sub- 
ject to  spherical  aberration  than  similar  lenses  of  glass. 

But  although  eye  pieces,  on  account  of  their  small  size,  may 
sometimes  be  made  of  the  precious  gems,  yet  this  can  rarely  be  the 
case  on  account  of  the  great  expense  attending  them.  It  is  obvious 
also  that  they  cannot  be  employed  for  the  object  lenses.  The  most 
successful  method  of  diminishing  spherical  aberration  in  eye  pieces 
of  glass,  is  by  a  combination  of  plano-convex  lenses,  by  means  of 
which  a  given  refracting  power  may  be  attained  with  far  greater  dis- 
tinctness than  by  a  single  lens  of  the  same  power.  Thus,  when  two 
plano-convex  lenses  are  placed  as  in  Fig.  125,  it  is  found  that  the 
image  has  four  times  the  distinct- 
ness of  a  double  convex  lens  of 
equivalent  power.*  Here  F  is 
a  lens  which  would  bring  the  G  -C... 
parallel  rays  to  a  focus  and  form 
the  image  at  the  distance  of  G ; 

*  The  Scioptic  Ball,  used  in  the  camera  obscura,  (Art.  524.)  is  form- 
ed of  two  such  lenses. 

41 


322  OPTICS. 

but  E  is  another  similar  lens,  which,  receiving  them  in  a  converging 
state,  makes  them  converge  more  and  come  to  a  focus  at  H.  The 
double  convex  lens  D  would  do  the  same,  but  with  much  greater 
spherical  aberration.  It  appears,  indeed,  that  the  spherical  aberra- 
tion may  be  wholly  removed  by  combining  a  meniscus  with  a  double 
convex  lens  of  certain  curvatures. 

559.  In  object  glasses,  which,  on  account  of  their  smaller  curva- 
tures,  are  not  so  subject  to  error  from  spherical  aberration  as  eye 
glasses  are,  the  most  advantageous  form  is  that  of  a  double  convex 
lens  of  unequal  curvatures,   the  radii  of  the  opposite  surfaces  being 
as  one  to  six, -(Art.  504.)  and  the  flat  side  being  turned  towards  the 
parallel  rays. 

In  short  it  appears,  that  in  order  to  avoid  the  errors  arising  from 
spherical  aberration,  in  large  lenses,  they  must  be  made  as  thin  as 
convenience  will  permit ;  that  where  it  is  practicable,  they  may  be 
most  advantageously  formed  of  the  precious  gems,  particularly  the 
diamond ;  that  a  plano-convex  lens  with  its  convex  side  towards  the 
parallel  rays  has  less  aberration  than  a  double  convex  lens  of  equiv- 
alent power ;  that  two  plano-convex  lenses  may  be  so  combined  as 
to  have  only  one  fourth  as  much  aberration  as  the  double  lens,  and 
a  meniscus  may  be  so  united  to  a  double  convex  lens  as  wholly  to 
prevent  aberration ;  and  finally,  that  the  aberration  may  be  reduced 
to  a  very  small  error  simply  by  employing  a  double  convex  lens 
whose  curvatures  on  the  opposite  sides  are  as  1  to  6. 

Since  lenses  having  the  curvature  of  one  of  the  conic  sections  are 
free  from  spherical  aberration,  Sir  Isaac  Newton  ground  an  object 
glass  into  the  figure  of  a  paraboloid.  This  was  free  from  the  error 
in  question,  but  involved  another  still  more  formidable,  since  it  de- 
composed the  light  and  gave  an  image  tinged  with  the  colors  of  the 
rainbow.  On  observing  this,  Sir  Isaac  pronounced  the  farther  im- 
provement of  the  refracting  telescope  to  be  hopeless,  and  betook 
himself  to  exclusive  efforts  for  improving  the  reflecting  telescope. 
But  the  combined  ingenuity  of  philosophers  and  artists,  has  nearly 
overcomeahis  error  also. 

560.  The  next  difficulty,  therefore,  to  be  considered  is  that  which 
arises  from  the  separation  of  the  prismatic  colors,  in  consequence  of 


TELESCOPES.  323 

. 

the  different  refrangibility  of  the  different  rays,  an  error  which  is 
called  Chromatic  Aberration. 

The  general  principles  of  Chromatic  Aberration,  will  be  readily 
comprehended  by  calling  to  mind,  that  distinct  images  are  formed 
only  when  the  rays  of  the  same  pencil  which  flow  from  any  point  in 
the  object  are  collected  into  one  and  the  same  point  in  the  image, 
unmixed  with  rays  from  any  other  point ;  that  the  prismatic  rays 
which  compose  white  light  have  severally  different  degrees  of  re- 
frangibility, some  being  more  turned  out  of  their  course  than  others, 
in  passing  through  the  same  medium ;  that,  consequently,  the  differ- 
ent colored  rays  of  the  same  pencil  would  meet  in  different  points, 
each  set  of  colored  rays  forming  its  own  image,  but  all  these  images 
becoming  blended  with  one  another,  and  thus  composing  a  confused, 
colored  picture. 

To  illustrate  these  prin-  Fig.  126. 

ciples  let  LL  be  a  lens  of 
crown  glass,  and  RL,  RL. 
rays  of  white  light  incident 
upon  it,  parallel  to  its  axis 
Rr.  Let  the  extreme  vio- 
let rays  be  refracted  so  as  to  meet  the  axis  in  v  ;  then  the  extreme 
red  will  meet  the  axis  at  some  point  more  distant  from  the  lens,  as 
at  r.  Cv  and  Cr  are  the  focal  distances  of  the  lens  for  the  violet 
and  the  red  rays  respectively.  The  distance  m  is  the  chromatic 
aberration,  and  the  circle  whose  diameter  is  ab}  which  passes  through 
the  focus  of  the  mean  refrangible  rays  at  0,  is  called  the  circle  of 
least  aberration. 

561.  It  is  clear  from  these  observations,  that  the  lens  will  form  a 
violet  image  of  the  sun  at  v,  a  red  image  at  r,  and  images  of  the 
other  colors  of  the  spectrum  at  intermediate  points  between  r  and  v; 
so  that  if  we  place  the  eye  behind  these  images,  we  shall  see  a  con- 
fused image,  possessing  none  of  that  sharpness  and  distinctness  which 
it  would  have  had  if  formed  only  by  one  kind  of  rays. 

The  separation  of  white  light  into  its  prismatic  colors,  is  called 
Dispersion  ;  and  the  comparative  power  of  effecting  this  separation, 
possessed  by  different  media,  is  called  the  Dispersive  power.  The 
dispersive  power  is  measured  by  the  ratio  which,  in  any  case,  the 


324  OPTICS. 

separation  of  the  red  arid  violet  rays  bears  to  the  mean  refraction 
of  the  compound  ray.  Thus,  if  a  ray  of  solar  light  on  passing 
through  a  lens,  is  turned  out  of  its  original  direction  27°,  and  the 
red  and  violet  rays  are  separated  from  each  other  1°,  then  the  dis- 
persive power  is  said  to  be  ^T,  which  is  usually  expressed  in  the 
form  of  a  decimal  fraction,  .037 =^T. 

562.  Different  bodies  possess  different  dispersive  powers. 

The  dispersive  powers  of  a  few  of  the  most  important  substances 
in  relation  to  the  subject  before  us,  are  exhibited  in  the  following 
table. 

Dispersive  Power.  Dis.  Power. 

Oil  of  Cassia,  0.139  Plate  Glass,  0.032 

Sulphuret  of  Carbon,      0.130  Sulphuric  Acid,  0.031 

Oil  of  Bitter  Almonds,  0.079  Alcohol,  0.029 

Flint  Glass,  0.052  Rock  Crystal,  0.026 

Muriatic  Acid,  0.043  Blue  Sapphire,  0.026 

Diamond,  0.038  Fluor  Spar,  0.022 

Crown  Glass,  (green,)    0.036 

From  this  table  it  appears,  that  the  transparent  substances  which 
have  the  highest  dispersive  power,  are  the  oil  of  cassia  and  the  sul- 
phuret  of  carbon,*  both  of  which  fluids  have  been  made  to  perform 
an  important  service  in  the  construction  of  achromatic  telescopes ; 
that  flint  glass,  as  that  used  for  decanters,  has  a  much  higher  disper- 
sive power  than  crown  glass,  or  that  which  is  analogous  to  window 
glass ;  that  the  diamond  has  a  low  dispersive  power,  but  is  exceeded 
in  this  respect  by  rock  crystal,  the  sapphire,  and  fluor  spar,  which 
last  bodies  have  the  least  dispersive  power  of  any  known  substances. 

563.  With  these  facts  in  view,  we  may  now  inquire  by  what  means 
the  object  glass  of  the  telescope  is  rendered  achromatic. 

If  we  place  behind  LL  (Fig.  126.)  a  concave  lens  GG  of  the 
same  glass,  and  having  its  surfaces  ground  to  the  same  curvature, 
such  a  lens  having  properties  directly  opposite  to  those  of  the  con- 
vex lens  will  neutralize  its  effects.  Consequently,  the  rays  which 


A  limpid  fluid  prepared  from  sulphur  and  charcoal. 


TELESCOPES.  325 

were  separated  into  their  prismatic  colors  by  the  convex  lens  will  be 
reunited  by  the  concave  lens,  and  reproduce  white  light.  But  though 
such  a  combination  of  the  two  lenses  will  correct  the  color,  yet  it  also 
destroys  the  power  of  the  convex  lens  to  form  an  image,  on  which 
its  use  solely  depends.  Could  we  find  a  concave  lens  which  would 
correct  all  the  color  and  yet  not  destroy  this  refracting  power,  the 
two  lenses  would  evidently  form  the  achromatic  combination  sought 
for.  Now  this  is  what  is  actually  done  :  by  making  the  concave  lens 
of  a  substance  which  has  a  higher  dispersive  power  than  that  of  which 
the  convex  lens  is  made,  the  curvature  of  the  concave  lens  will  not 
need  to  be  so  great  as  that  of  the  convex  lens,  and  of  course  the  two 
together,  constituting  the  compound  lens,  will  be  equivalent  in  refract- 
ing power  to  a  single  lens,  whose  convexity  is  equal  to  the  difference 
of  their  curvatures.  The  most  common  combination  is  that  of  flint 
glass  with  crown  glass,  the  concave  lens  being  made  of  flint  glass, 
and  the  convex  of  crown.  By  the  table  in  Art.  562,  it  will  be  seen 
that  the  dispersive  power  of  flint  glass  is  52  while  that  of  crown  glass 
is  36,  which  numbers  are  nearly  as  3  to  2,  and  these  numbers,  there- 
fore, may  be  employed  for  the  sake  of  illustration.  Since  the  power 
of  the  concave  lens  to  reunite  the  prismatic  rays  is  so  much  greater 
than  that  of  the  convex  lens  to  separate  them,  we  shall  not  require 
a  refractive  power  to  effect  this  equivalent  to  that  of  the  convex  lens; 
that  is,  a  concave  lens  of  less  curvature  and  proportionally  greater 
focal  distance,  will  serve  our  purpose.  Therefore, 

An  achromatic  lens  is  formed  by  the  union  of  a  convex  and  a  con- 
cave lens,  whose  dispersive  powers  are  respectively  proportional  to 
their  focal  distances. 

564.  A  telescope  furnished  with  an  object  glass  thus  formed,  is 
called  an  Achromatic  Telescope.  The  spherical  aberration  being 
corrected  by  the  methods  pointed  out  in  Art.  557,  and  the  chro- 
matic aberration  being  destroyed  in  the  manner  above  described,  the 
Refracting  Telescope  becomes  an  instrument  of  great  perfection, 
and  is  reckoned  among  the  greatest  works  of  art.  Until  recently, 
it  was  rare  to  meet  with  Refracting  Telescopes  of  an  aperture  of 
more  than  from  three  to  five  inches.  For  we  have  already  seen 
that  the  errors  of  spherical  and  chromatic  aberration  increase  rapid- 
ly as  the  size  of  the  aperture  is  augmented. 


326  OPTICS. 

565.  If  it  be  asked,  what  is  the  use  of  a  large  aperture,  since  the 
magnifying  power  does  not  depend  upon  the  diameter  of  the  object 
glass,  but  upon  the  ratio  between  the  focal  distance  of  the  object 
glass  and  the  focal  distance  of  the  eye  glass,  (Art.  554.)  we  answer, 
that  the  use  of  a  large  aperture  is  to  admit,  condense,   and  finally 
convey  to  the  eye,  a  larger  beam  of  light,   and  thus  to  render  many 
objects,  as  the  smaller  stars,  or  Jupiter's  belts,  visible,   which  other- 
wise would   not  be  so,  on  account  of  the  feebleness  of  the  light 
which  they  transmit  to  us.     Want  of  light  is  in  fact  one  of  the  great- 
est difficulties  that  the  telescope  has  to  contend  with ;  for,  in  the  first 
place,  the  object  glasses  of  most  telescopes  are  comparatively  small, 
and  are  necessarily  so  on  account  of  the  difficulty  of  procuring  suit- 
able glass  for  those  of  a  larger  size ;  and  in  the  second  place,  of  the 
light  admitted  through  the  object  glass,  a  great  proportion  is  inter- 
cepted and  wasted  in  various  ways,  many  instruments  being  able  to 
save  only  the  central  rays  without  rendering  the  image  indistinct  and 
colored.     Thus,  when  very  high  magnifiers  are  applied,  (which  of 
course  have  very  small  focal  distances,)  the  rays  proceed  from  the 
focus  and  fall  upon  the  microscope  so  obliquely,  that  only  those 
which  pass  through  the  central  parts  of  the  lens  can  be  saved,  since 
such  as  fall  upon  the  marginal  parts  of  the  lens  are  too  much  affect- 
ed by  spherical  and  chromatic  aberration,  to  form  with  the  others  a 
distinct  and  colorless  image. 

566.  Want  of  field  of  view  is  another  difficulty  to  be  surmounted. 
When  we  use   an  object  glass  of  short  focus  with  a  high  magnifier, 
the  microscope  must  have  a  focus  proportionally  short,  and  of  course 
the  field  of  view  will  be  very  limited  and  the  light  but  feeble.    This 
difficulty  may  be  obviated  by  using  an  object  glass  of  very  great  fo- 
cal distance.     If,  for  example,  the  focal  distance  of  the  object  glass 
were  only  12  inches,  in  order  to  attain  a  magnifying  power  of  120, 
we  must  employ  a  microscope  whose  focal  distance  is  only  y^th  of 
an  inch.     But  if  the  focal  distance  of  the  object  glass  were  10  feet, 
or  120  inches,  then  our  microscope  might  have  a  focal  distance  of 
1  inch,  jyhich  would  give  a  larger  field  and  a  stronger  light.     With 
the  view  of  obviating  several  of  the  foregoing  difficulties,  the  earlier 
astronomers  who  used   the  telescope,  employed  their  object  glasses 
lenses  whose  focal  lengths  were  very  great.     Cassini,  an  Italian  as- 


TELESCOPES.  327 

tronomer,  constructed  telescopes  eighty,  one  hundred,  and  one  hun- 
dred and  thirty  six  feet  long ;  and  Huygens  employed  such  as  were 
nearly  the  same  length.  The  latter  astronomer  dispensed  with  the 
tube,  fixing  his  object  glass,  contained  in  a  short  tube,  to  the  top  of 
a  high  pole,  and  forming  the  image  in  the  air  near  the  level  of  the 
eye,  which  image  he  viewed  with  an  eye  glass,  as  usual.  With  tele- 
scopes of  this  description,  several  of  the  satellites  of  Saturn  were 
discovered. 

567.  But  one  of  the  most  formidable  difficulties  hitherto  encoun- 
tered in  the  construction  of  large  Refracting  Telescopes,  has  arisen 
from  the  imperfections  of  glass.  When  Dollond  (the  Engljsh  artist 
who  first  perfected  the  Achromatic  Telescope,)  engaged  in  the  manu- 
facture of  his  instruments,  he  fortunately  had  possession  of  a  consid- 
erable quantity  of  very  fine  glass ;  but  when  that  was  used  up,  no 
more  of  equal  quality  could  be  obtained  in  England.*  On  the  con- 
tinent, however,  one  or  two  celebrated  artists  have  been  more  suc- 
cessful. The  most  distinguished  manufacturer  of  optical  glass  was 
M.  Guinand  of  Switzerland,  who  died  in  1823.  He  greatly  excelled 
all  his  predecessors  or  cotemporaries  in  fabricating  large  masses  of 
perfectly  homogeneous  glass.  But  even  he  could  produce  disks  of 
twelve  or  eighteen  inches  in  diameter  in  no  other  way,  than  by  se- 
lecting the  purest  specimens  of  smaller  pieces,  and  joining  them  to- 
gether. In  1805,  M.  Fraunhofer  of  Bavaria,  a  celebrated  manu- 
facturer of  telescopes,  invited  Guinand  to  become  his  associate  in 
the  manufacture  of  optical  glass;  and  from  the  united  efforts  of  these 
most  ingenious  men,  proceeded  glass  of  unexampled  transparency 
and  purity.  Fraunhofer  has  recently  deceased,  and  the  difficulty  of 
procuring  perfect  glass  is  renewed.  This  induced  the  Royal  Society 
of  London  to  appoint  a  committee  to  institute  new  experiments  on 
this  subject.  These  have  been  prosecuted  with  the  greatest  ability, 
but  have  as  yet  produced  no  important  results. 

"  *  The  present  Mr.  Dollond,  a  successor  of  the  inventor  of  Achro- 
matic Telescopes,  "  has  not  been  able  to  obtain  a  disk  of  flint  glass 
four  inches  and  a  half  in  diameter,  fit  for  a  telescope,  within  the  last 
five  years,  or  a  similar  disk  of  five  inches  diameter  within  the  last 
ten  years." — Faraday,  Phil.  Trans.  1830, 


328  OPTICS. 

568.  These  circumstances  we  have  thought  worthy  of  being  reci- 
ted in  order  to  impress  on  the  mind  of  the  learner  the  formidable  na- 
ture, as  well  as  the  great  number,  of  the  difficulties  to  be  overcome 
in  the  construction  of  a  large  Achromatic  Telescope.     Yet  they  have 
in  several  instances,  been  completely  surmounted.     Fraunhofer  ex- 
ecuted two  telescopes  with   achromatic  object  glasses,  the  one  nine 
inches  and  nine  tenths,  and  the  other  twelve  inches  in  diameter ;  and 
at  the  period  of  his  death  he  was  proposing  to  undertake  one  eight- 
een inches  in  diameter.     That  of  9.9  inches  aperture  was  made  for 
the  Russian  government  for  the  use  of  the  observatory  at  Dorpat, 
where  under  the  direction  of  M.  Struve,  a  distinguished  astronomer, 
it  has  ajready  achieved  several  valuable  discoveries  in  astronomy. 
The  object  glass  has  a  focal  length  of  twenty  five  feet.     The  con- 
cave part  of  the  compound  lens  is  formed  of  a  dense  flint  glass  made 
by  Guinand,  and  has  a  greater  dispersive  power  than  any  obtained 
before.     It  is  perfectly  free  from  veins,  and  nearly  from  every  impu- 
rity.    The  instrument  has  four  eye  glasses  varying  in  magnifying 
power  from  one  hundred  and  seventy  five  to  seven  hundred.* 

569.  The  great  difficulty  of  procuring  perfect  glass  for  achro- 
matic telescopes  has  led  opticians  to  attempt  the  construction  of  len- 
ses for  this  purpose  out  of  some  transparent  fluid  which  might  be  in- 
closed -in  thin  glass.     Such  a  medium  seemed  peculiarly  suited  to 
take  the  place  of  the  concave  lens  in  which  the  principal  difficulty 
resides.     Professor  Barlow,  of  the  Military  Academy  of  Woolwich, 
has  recently  made  several  telescopes  on  this  principle,  the  last  of 
which  had  an  aperture  of  7.8  inches,  and  performed  as  well  as  the 
larger  kind  of  achromatic  telescopes  constructed  in  the  usual  way. 
The  fluid  employed  for  this  purpose  was  the  sulphuret  of  carbon,   a 
limpid  fluid  prepared  from  sulphur  and  charcoal.     It  is  singularly 
adapted  to  optical  purposes,  having  a  refracting  power  about  equal  to 
that  of  the  best  flint  glass,  with  a  dispersive  power  more  than  double 


*  It  is  said  that  as  a  general  rule,  Achromatic  Telescopes]are  priced 
in  the  i^io  of  the  cube  of  the  aperture.  If  a  telescope  with  an  ob- 
ject glass  three  inches  in  diameter,  is  valued  at  five  hundred  dollars, 
one.  of  twelve  inches  would  cost  sixty  four  times  as  much,  that  is,  thir- 
ty two  thousand  dollars. 


TELESCOPES.  329 

that  of  the  same  substance.  It  is,  moreover,  perfectly  colorless, 
beautifully  transparent,  and  although  it  is  very  volatile  yet  when  close- 
ly sealed  it  possesses  nearly  the  same  optical  properties  under  all  re- 
quired temperatures.  The  advantages  of  using  sulphuret  of  carbon 
should  the  experiments  finally  succeed  as  well  as  is  expected,  are  the 
following  : 

1.  It  renders  us  independent  of  flint  glass. 

2.  It  enables  us  to  increase  the  aperture  of  the  telescope  to  a  very 
considerable  extent. 

3.  It  gives  us  all  the  light,  field  and  focal  power  of  a  telescope  of 
one  and  a  half  times  at  least,  probably  twice  the  length  of  the  tube. 

4.  The  expense  of  large  telescopes  (which  consists  mainly  in  the 
cost  of  the  object  glass)   is  greatly  diminished,  the  most  expensive 
part  being  supplied  with  less  than  one  ounce  of  sulphuret  of  carbon 
of  the  value  of  three  shillings. 

The  Terrestrial  or  Day  Telescope. 

570.  As  the  Astronomical  Telescope  represents  objects  inverted, 
it  requires  to  be  so  modified  for  terrestrial  views,  that  objects  may 
appear  erect.  This  is  effected  by  the  addition  of  two  more  lenses  of 
similar  figure  to  that  of  the  eye  glass,  and  of  the  same  focal  length. 
The  first  of  these  additional  glasses  forms  a  second  image  of  the  ob- 
ject inverted  with  respect  to  the  first  image  and  therefore  erect  with 
respect  to  the  object.  This  image  is  viewed  by  the  second  glass  33 
by  any  simple  microscope.  Thus,  AB,  the  object  glass  forms  an  in- 


M 


li 


verted  image  nm  of  the  object  MN.  Instead  of  viewing  this  image 
by  the  eye  placed  at  L,  as  in  the  common  astronomical  telescope, 
we  suffer  the  pencil  of  parallel  rays  to  cross  each  other  at  L  and  fall 
upon  a  second  lens  EF  (similar  in  all  respects  to  CD)  which  collects 
them  into  an  image  m'n'  in  its  focus  of  parallel  rays,  which  image  is 

42 


330  OPTICS. 

viewed  by  the  eye  glass  GH  in  the  same  manner  as  the  object  itself 
would  be. 

As  some  portion  of  the  light  is  reflected,  and  some  absorbed  and 
dissipated  by  passing  through  these  additional  lenses,  they  of  course 
diminish  the  brightness  of  the  view ;  but  in  the  day  time  there  will 
usually  be  light  enough  for  distinct  vision  after  this  loss  is  sustained y 
while  it  is  more  agreeable  and  convenient  to  have  the  objects  present- 
ed to  us  in  their  natural  positions  than  inverted.  It  will  be  remarked 
that  the  additional  lenses  do  not  magnify,  the  focal  length  of  each 
being  the  same  as  that  of  the  first  eye  glass.  Were  they  rendered 
smaller  for  the  purpose  of  magnifying,  the  field  of  view  and  the  light 
would  both  be  impaired. 

571.  We  usually  find  in  telescopes,  particularly  those  designed 
for  terrestrial  objects,  some  contrivance,  as  a  draw  tube,  by  which  the 
eye  glass  can  be  brought  nearer  to,  or  withdrawn  from  the  object- 
glass.  This  is  to  accommodate  the  instrument  to  objects  at  different 
distances.  When  it  is  directed  to  very  near  objects,  the  image  is 
thrown  farther  back,  and  therefore  in  order  that  it  may  be  in  the  fo- 
cus of  the  eye  glass,  (which  is  essential  to  distinct  vision)  the  latter 
must  be  drawn  backward ;  but  where  the  object  is  remote,  the  image 
is  formed  nearer  to  the  object  glass,  and  then  the  eye-glass  must  be 
moved  forward,  till  its  focus  of  parallel  rays,  comes  to  the  place  of 
the  image.  For  a  similar  reason,  near  sighted  persons  require  the 
eye-glass  to  be  brought  nearer  than  usual  to  the  object-glass;  for 
then  the  image  will  be  nearer  to  the  eye-glass  than  its  focus  of 
parallel  rays,  and  the  rays  will  meet  the  eye  diverging,  a  condition 
favorable  to  eyes  naturally  too  convex.  For  a  contrary  reason,  long 
sighted  persons,  who  usually  wear  convex  spectacles,  may  adjust  the 
telescope  to  suit  their  eyes  without  spectacles,  by  removing  the  eye- 
glass farther  back  than  usual. 

Most  terrestrial  telescopes  contain  a  greater  number  of  glasses 
than  are  represented  in  Fig.  127.  Such  a  number  are  used  for  the 
purpose  of  correcting  spherical  and  chromatic  aberration,  these  er- 
rors being  less  in  several  flat  and  thin  lenses  than  in  a  smaller  num- 
ber of  equivalent  lenses  of  greater  curvature. 

Astronomical  telescopes  are  easily  adapted  to  terrestrial  observa- 
tions, by  removing  the  eye  glass  and  substituting  a  tube  containing 
the  additional  glasses  for  rendering  the  view  erect. 


TELESCOPES. 


Reflecting  Telescopes. 


331 


572.  Reflecting  Telescopes  differ  in  principle  from  those  already- 
described  only  in  forming  their  image  by  a  concave  reflector,  instead 
of  a  convex  object-glass.  The  most  common  form  of  the  Reflect- 
ing Telescope,  is  the  Gregorian,  so  called  from  the  inventor,  Dr. 
James  Gregory,  of  Scotland.  The  general  principles  of  this  instru- 
ment may  be  explained  as  follows : 

In  the  Gregorian  Telescope,  the  light  (supposed  to  come  in  par- 
allel rays)  is  first  received  by  a  large  concave  speculum,  by  which  it 
is  brought  to  a  focus  and  made  to  form  an  inverted  image.  On  the 
opposite  side  of  this  image,  and  facing  the  large  speculum,  is  placed 
a  small  concave  speculum,  of  greater  curvature,  at  such  a  distance 
from  the  image  that  the  rays  proceeding  from  it  and  falling  on  the 
speculum  are  made  to  converge  to  a  focus  situated  a  small  distance 
behind  the  large  speculum,  passing  through  a  circular  aperture  in 
the  center  of  it.  This  second  image  is  magnified  by  a  microscope 
as  in  the  Refracting  Telescope.  This  description  may  now  be  ap- 
plied to  the  annexed  figure. 

Fig.  128. 
A  B 


ABCD,  a  large  open  tube  of  brass,  iron,  or  mahogany  to  contain 
the  reflectors. 

abed,  a  smaller  tube  to  receive  the  second  image  and  the  eye  glass. 

EE,  large  concave  speculum,  usually  composed  of  a  metallic  com- 
pound called  speculum  metal. 

FF,  small  concave  speculum. 

win,  image  formed  by  the  large  reflector. 

nm,  image  formed  by  the  small  reflector. 

G,  eye  glass. 

WY,  a  metallic  rod  having  a  screw  connected  with  the  small  re- 
flector, by  means  of  which  this  reflector  is  made  to  approach  the  first 
image  or  to  recede  from  it. 


332  OPTICS. 

Some  of  the  pencils  of  rays  necessary  to  form  the  respective  ima- 
ges are  omitted  in  the  figure  to  prevent  confusion. 

573.  From  the  foregoing  construction  it  is  evident,  first,  that  the 
image  viewed  by  the  eye  being  in  the  same  position  with  the  object, 
the  latter  will  appear  erect;  secondly,  that  since  the  mirrors  may  be 
formed  of  a  parabolic  figure,*  all  spherical  aberration  may  be  easi- 
ly prevented  ;  thirdly,  that  since  light  is  not  decomposed  by  reflex- 
ion,  reflecting  telescopes  are  not  subject  to  chromatic  aberration  : 
and,  hence,   that  it  is  not  necessary  to  lengthen  the  tube  as  the  ap- 
erture is  increased,  as  is  the  case  in  refracting  telescopes  (Art. 
566.) ;  but  since  the  light  will  depend,  chiefly,  on  the  size  of  the 
large  reflector,  a  strong  light  may  be  obtained  with  a  comparatively 
short  tube.     The  achromatic  telescope,  however,  with  all  the  latest 
improvements,  is  deemed  a  more  perfect  and  more  convenient  in- 
strument than  the  reflecting  telescope ;  and  it  is  supposed  that  there 
will  be  no  occasion  hereafter  to  construct  reflectors  of  such  enor- 
mous dimensions  as  those  of  Dr.  Herschel.     Some  account  of  his 
forty  feet  reflector  may  form  a  suitable  close  to  this  sketch  of  optical 
instruments. 

574.  Under  the  munificent  patronage  of  George  III,  Sir  William 
Herschel  began,  in  1785,  to  construct  a  telescope  forty  feet   long, 
and  in  1789,  on  the  day  when  it  was  completed,  he  discovered  with 
it  the  sixth  satellite  of  Saturn.     The  great  speculum  was  more  than 
four  feet  in  diameter,   and  weighed  two  thousand  one  hundred  and 

eighteen  pounds.     Its  focal  length  was  forty  feet.     The  tube  which 
contained  it  was  made  of  sheet  iron. 

The  light  afforded  by  this  instrument  was  astonishingly  great. 
The  largest  fixed  stars,  as  Sirius,  shone  in  it  with  the  splendor  of 
the  sun.  The  reason  of  this  will  be  obvious  when  we  reflect  that  it 
collected  and  conveyed  to  the  eye,  in  the  place  of  the  Small  beam 
that  enters  the  naked  organ,  a  beam  of  light  from  the  star  more  than 
four  feet  in  diameter.  Hence  it  was  suited  to  reveal  to  the  eye 
numberless  stars  and  clusters  of  stars,  which  preceding  telescopes 
had  failed  t<5  exhibit,  because  they  could  not  collect  a  sufficient  quan- 


An  elliptical  figure  has  the  same  properly 


TELESCOPES.  333 

tity  of  their  light.  To  economize  the  light  to  the  best  advantage,  the 
small  mirror  employed  in  the  Gregorian  telescope  (see  Fig.  128.) 
was  dispensed  with,  since  every  successive  reflexion  dissipates  a  con- 
siderable portion  of  the  light,  and  the  image  was  thrown  near  to  the 
open  mouth  of  the  tube,  where  it  was  viewed  by  the  eye-glass  direct- 
ly, the  observer  being  seated  so  as  to  look  into  the  mouth  in  front.  In- 
order  to  prevent  the  head  from  obstructing  too  much  of  the  light, 
the  image  was  formed  near  one  side  of  the  tube.  Its  greatest  mag- 
nifying power  was  six  thousand  four  hundred  and  fifty ;  but  this  was 
used  only  for  the  smallest  stars. 

This  great  telescope  was  mounted  out  of  doors  in  a  frame  of  pro- 
portional size ;  but  by  exposure  to  the  weather,  the  frame  has  re- 
cently become  so  much  decayed  that  it  has  been  taken  down  and 
another  telescope  of  twenty  feet  focus  erected  in  its  place,  with  which 
Sir  J.  Herschel  is  prosecuting,  with  great  success,  the  researches  of 
his  father. 


APPENDIX. 


OF    PHILOSOPHICAL    APPARATUS    AND    EXPERIMENTS. 

THE  utility  of  experiments  for  verifying  the  truths  of  philosophy, 
and  for  impressing  them  upon  the  memory  of  the  learner,  is  univer- 
sally acknowledged.  Experiments,  indeed,  constitute  the  true  and 
legitimate  kind  of  entertainment,  by  which  the  dryer  and  less  attract- 
ive parts  of  this  science  are  to  be  rendered  acceptable  and  pleasing 
to  the  young  learner. 

In  most  of  our  schools,  however,  few  or  no  experiments  are  given 
in  connexion  with  the  study  of  Natural  Philosophy,  either  from  the 
want  of  suitable  apparatus,  or  of  leisure  or  inclination  on  the  part  of 
the  instructor. 

Although  accurate  and  expensive  instruments  are  highly  useful  for 
the  purpose  of  verifying  the  doctrines  of  philosophy,  still,  numerous 
and  useful  illustrations  of  philosophical  principles  may  be  exhibited 
by  apparatus  of  an  inferior  kind,  such  as  can  be  constructed  under 
the  direction  of  the  experimenter  himself,  by  ordinary  mechanics. 
An  ingenious  artisan,  furnished  with  suitable  cuts  or  drawings,  with 
a  few  directions  from  the  teacher,  will  construct  many  plain  articles 
of  apparatus,  that  will  answer  the  purpose  nearly  as  well  as  more  ex- 
pensive instruments.  For  instruments  of  the  better  sort,  however, 
it  will  generally  be  found  more  advantageous  to  apply  to  professed 
instrument  makers,  a  number  of  whom  will  be  found  in  each  of  our 
large  cities. 

The  following  list  of  articles,  with  such  additions  as  every  one 
may  easily  make  for  himself,  will  be  sufficient  for  performing  the 
experiments  necessary  to  accompany  the  present  work. 

1.  dltwootfs  Machine,  (Fig.  2,  p.  16.) — This  is  one  of  the  most 
useful  articles  of  apparatus,  since  it  affords  the  means  of  verifying 
the  fundamental  principles  of  mechanics.  (See  pp.  16,  21,  and  34.) 
It  is,  however,  too  expensive  to  be  comprised  in  small  collections  of 
apparatus. 

2.  Whirling  Tables. — These  afford  an  instructive  exemplification 
of  the  principles  of  rotary  motion,  and  of  the  doctrine  of  centrifugal 
force. 

3.  Center  of  Gravity  Apparatus. — Several  articles,  of  the  nature 
of  toy*,  are  sold  at  the  instrument  maker's,  which  afford  a  pleasing 
illustration  of  the  doctrine  of  the  center  of  gravity. 

4.  Mechanical  Powers. — A  set  of  these,  in  brass,  connected  to- 
gether in  the  same  frame,  is  sold  in  the  shops.     They  afford  pleasing 
illustrations  of  the  principle  of  the  Lever,  the  Wheel  and  Axle,  &c. 


PHILOSOPHICAL    APPARATUS.  335 

The  principles  of  HYDROSTATICS  and  PNEUMATICS,  are  suscepti- 
ble of  very  striking  and  accurate  verification  by  means  of  suitable- 
apparatus. 

5.  Bent  Tube,  (Fig.  62.) — Or,  the  apparatus  represented  in  Fig. 
63,  may  be  easily  formed   by  inserting  into  a  strong  wooden  boxy 
made  water-tight,  glass  tubes,  or  vessels  of  almost  any  shape,  as  a 
broken  decanter,  or  glass  receiver. 

6.  Hydrostatic  Paradox,  (Fig.  54.) — This  may  be  made  by  a 
saddler,  or  better  by  a  professed  bellows-maker.     Two  circular  pie- 
ces of  hard,  close-grained  wood,  eighteen  inches  in  diameter  and 
two  inches  thick,   are  used  for  the  top  and  bottom.     To  these  is 
nailed  a  piece  of  the  strongest  leather,  well  soaked  with  oil,  or  satu- 
rated with  melted  tallow.     The  glass  tube,  instead  of  ascending; 
from  the  side,  as  represented  in  figure  64,  may  more  conveniently 
be  attached  to  a  large  screw  inserted  in  the  top  board,  near  one 
side.     This  may  be  unscrewed  for  the  purpose  of  introducing  water. 
The  glass  tube  may  be  about  three  feet  long,  and  of  quarter  inch  bore. 
Although  very  heavy  weights  may  be  raised  by  a  small  quantity,  as 
half  a  gill,  of  water,  yet  they  rise  through  so  small  a  space  as  hardly 
to  be  perceptible,   and  the  experiment  is  not  sufficiently  striking  to 
interest  the  spectator.     The  motion,  however,  may  be  multiplied  by 
connecting  a  lever  arid  multiplying  wheels  with  the  bellows,  by  which 
means  a  very  small  motion  of  the  bellows  will  give  a  rapid  revolution 
to  a  pointer,  and  thus  render  the  verification  of  the  doctrine  entirely 
satisfactory.     Such  a  multiplying  apparatus  has  been  connected  with 
the  bellows  belonging  to  the  apparatus  of  Yale  College,  that  half  a 
gill  of  water  will  communicate  a  rapid  motion  to  a  pointer,  when  the 
bellows  is  loaded  with  a  weight  equivalent  to  ten  fifty-sixes,  or  five 
hundred  and  sixty  pounds. 

7.  Specific  Gravity  Apparatus. — A  box  of  instruments  under  this 
name  is  sold  in  the  shops ;  but  an  accurate  pair  of  scales  and  weights, 
a  hook  being  attached  to  the  bottom  of  one  of  the  scales,  is  all  thai 
is  absolutely  required,  beyond  such  apparatus  as  every  one  may 
command. 

8.  Air  Pump,  (Fig.  68.) — A  double  barrelled  air-pump,  of  the 
kind  represented  in  figure  68,  with  the  various  appendages  that  usu- 
ally accompany  it,  is  a  most  important  article  of  philosophical  ap- 
paratus.    The  experiments  performed  with  it,  upon  the  pressure 
and  elasticity  of  the  air,  are  easy  to  the  experimenter,  and  novel, 
entertaining,  and  instructive  to  the  learner.     The  barrels  are  some- 
times made  of  glass  instead  of  brass,  which  has  the  advantage  of 
rendering  the  process  of  exhaustion  visible  to  the  learner.     Such 
barrels  are  also  preferable  to  those  of  brass,  on  account  of  their 
being  less  liable  to  corrode  from  the  action  of  the  oil  employed  to 
soften  the  valves  and  tighten  the  juncture  of  the  piston. 

9.  Condensing  Syringe,  (Fig.  70.) — Sometimes  a  copper  bottle 
furnished  with  several  spouts  for  projecting  water  in  different  shaped 


336  PHILOSOPHICAL    APPARATUS. 

jets,  is  sold  with  the  condensing  syringe.     This  apparatus  is  useful  for 
illustrating  the  principles  of  spouting  fountains,  the  fire  engine,  &c. 

10.  Barometer. — The  mountain  barometer,  which  is  adapted  ei- 
ther for  indicating  changes  of  weather,  or  for  taking  heights,   is  the 
kind  to  be  preferred.     Jt  would  be  conducive  to  the  interests  of  sci- 
ence, for  every  literary  institution  to  keep  an  accurate  daily  register 
of  the  states  of  the  barometer  and  thermometer. 

11.  Syphon  Tube. — A  common  glass  tube,  bent  over  a  dish  of 
coals,  will  answer  every  purpose  of  a  syphon. 

12.  Pump  Models,  (Figs.  74.  75.) 

13.  Model  of  the  Steam  Engine. — This  will  be  found  highly  in- 
structive and  interesting  to  pupils.     They  are  made  of  various  forms, 
but  are  usually  somewhat  expensive. 

14.  Electrical  Machines,  (Figs.  80.  81.)— The  subject  of  elec- 
tricity, can  scarcely  be  understood  without  experiments.     A  consid- 
erable number  of  these,  however,  can  be  performed  with  such  a  hum- 
ble  apparatus  as  that  described  on  page  202 ;  but  a  well  selected 
electrical  apparatus  is  not  very  expensive,  and  is  a  great  ornament  to 
a  collection.     Nearly  all  the  articles  represented  in  the  figures  under 
the  head  of  Electricity  are  required,  together  with  several  that  are 
mentioned  in  the  text. 

15.  Horse-shoe  Magnet. — A  large  magnet  of  this  kind  will  be  suf- 
ficient for  verifying  the  most  important  laws  of  magnetism. 

16.  Jl  concave  and  a  convex  Mirror. 

17.  Two  Prisms. 

18.  Perspective  Glass,  (Fig.  120.) — The  lens  belonging  to  this 
instrument,  (the  mirror  being  taken  off,)  will  be  found  very  conven- 
ient for  experiments  on  refraction,  being  ready  mounted  on  a  stand. 

19.  Microscope. — One  or  two  single  microscopes  of  different  pow- 
ers, will  be  sufficient  to  illustrate  the  theory  of  the  instrument. 

20.  Magic  Lantern. — This  apparatus  with  transparent  figures,  is 
not  expensive,  and  affords  a  pleasing  exemplification  of  the  magnify- 
ing power  of  lenses. 

21.  Solar  Microscope. — This  is  a  very  interesting  piece  of  appa- 
ratus, and  should  accompany  every  collection  where  the  expense  can 
be  afforded. 

22.  Achromatic  Telescope. — A  telescope  of  two  inches  aperture 
will,  if  well  constructed,   be  sufficient  to  afford   good  views  of  the 
moon  and  of  Jupiter's  satellites. 

The  expense  of  the  foregoing  apparatus  will  of  course  vary  with 
its  quality.  The  entire  collection,  made  in  the  best  manner,  would 
not  cost  more  than  one  thousand  dollars ;  and  when  constructed  in  a 
style  less  finished  and  elegant,  but  still  in  such  a  way  as  to  answer 
the  purpose  of  illustration,  the  cost  might  be  as  low  as  five  hundred 
dollars.  Taking  out  Atwood's  Machine,  the  model  of  the  Steam 
Engine,  and  the  Telescope,  the  remaining  articles  would  not  cost 
more  than  from  one  hundred  and  fifty  to  two  hundred  dollars. 


• 


Donewals  ana  — .  _..•*.  i 


Renewc 


Vs 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


U.C.BERKELEY  LIBRARIES 


' 


